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| {{distinguish|Grapheme|Graphane|Graphyne}} | {{distinguish|Grapheme|Graphane|Graphyne}} | ||
| {{technical|date=December 2013}} | {{technical|date=December 2013}} | ||
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| At the time of its isolation in 2004,<ref name="APS News"> | At the time of its isolation in 2004,<ref name="APS News"> | ||
| {{cite journal | {{cite journal | ||
| | |
|year=2009 | ||
| | |
|url=http://www.aps.org/publications/apsnews/200910/loader.cfm?csModule=security/getfile&pageid=187967 | ||
| | |
|title=This Month in Physics History: October 22, 2004: Discovery of Graphene | ||
| | |
|page=2 | ||
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|series=Series II |volume=18 |issue=9 | ||
| | |
|journal=] | ||
| }}</ref> researchers studying ] were already familiar with graphene's composition, structure and properties, which had been calculated decades earlier. The combination of familiarity, extraordinary properties, surprising ease of isolation and unexpectedly high quality of the obtained graphene enabled a rapid increase in graphene research. ] and ] at the ] won the ] in 2010 "for groundbreaking experiments regarding the ] material graphene".<ref> | }}</ref> researchers studying ] were already familiar with graphene's composition, structure and properties, which had been calculated decades earlier. The combination of familiarity, extraordinary properties, surprising ease of isolation and unexpectedly high quality of the obtained graphene enabled a rapid increase in graphene research. ] and ] at the ] won the ] in 2010 "for groundbreaking experiments regarding the ] material graphene".<ref> | ||
| {{cite web | {{cite web | ||
| | |
|title=The Nobel Prize in Physics 2010 | ||
| | |
|url=http://nobelprize.org/nobel_prizes/physics/laureates/2010/ | ||
| | |
|publisher=] | ||
| | |
|accessdate=2013-12-03 | ||
| }}</ref> | }}</ref> | ||
| {{toclimit|3}} | {{toclimit|3}} | ||
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| == Definition == | == Definition == | ||
| "Graphene" is a combination of ] and the suffix ], named by ],<ref name="termorigin">{{cite journal |doi= |
"Graphene" is a combination of ] and the suffix ], named by ],<ref name="termorigin">{{cite journal |doi=10.1351/pac199466091893 |first=H. P. |last=Boehm |first2=R. |last2=Setton |first3=E. |last3=Stumpp |title=Nomenclature and terminology of graphite intercalation compounds |url=http://www.iupac.org/publications/pac/1994/pdf/6609x1893.pdf |format=PDF |journal=Pure and Applied Chemistry |volume=66 |issue=9 |year=1994 |pages=1893–1901 }}</ref> who described single-layer carbon foils in 1962.<ref name="Boehm1962"> | ||
| {{cite journal | |
{{cite journal |first=H. P. |last=Boehm |first2=A. |last2=Clauss |first3=G. O. |last3=Fischer |first4=U. |last4=Hofmann |title=Das Adsorptionsverhalten sehr dünner Kohlenstoffolien |journal=Zeitschrift für anorganische und allgemeine Chemie |volume=316 |issue=3–4 |year=1962 |pages=119–127 |doi=10.1002/zaac.19623160303}} | ||
| </ref> | </ref> | ||
| The term ''graphene'' first appeared in 1987<ref name="Mouras87"> | The term ''graphene'' first appeared in 1987<ref name="Mouras87"> | ||
| {{Cite journal | |
{{Cite journal |last=Mouras |first=S. |author2=''et al.'' |title=Synthesis of first stage graphite intercalation compounds with fluorides |journal=Revue de Chimie Minerale |url=http://cat.inist.fr/?aModele=afficheN&cpsidt=7578318 |volume=24 |page=572 |year=1987}} | ||
| </ref> to describe single sheets of graphite as one of the constituents of ]s (GICs); conceptually a GIC is a crystalline salt of the intercalant and graphene. The term was also used in early descriptions of ]s,<ref name="Saito92">{{Cite journal | |
</ref> to describe single sheets of graphite as one of the constituents of ]s (GICs); conceptually a GIC is a crystalline salt of the intercalant and graphene. The term was also used in early descriptions of ]s,<ref name="Saito92">{{Cite journal |last=Saito |first=R. |title=Electronic structure of graphene tubules based on C60|doi=10.1103/PhysRevB.46.1804 |journal=Physical Review B |volume=46 |page=1804 |year=1992|bibcode=1992PhRvB..46.1804S |issue=3 |last2=Fujita |first2=Mitsutaka |last3=Dresselhaus |first3=G. |last4=Dresselhaus |first4=M. }}</ref> as well as for epitaxial graphene<ref name="Forbeaux98">{{Cite journal |last=Forbeaux |first=I. |title=Heteroepitaxial graphite on 6H-SiC(0001): Interface formation through conduction-band electronic structure |doi=10.1103/PhysRevB.58.16396 |journal=Physical Review B |volume=58 |page=16396 |year=1998 |bibcode=1998PhRvB..5816396F |issue=24 |last2=Themlin |first2=J.-M. |last3=Debever |first3=J.-M. }} | ||
| </ref> and polycyclic aromatic hydrocarbons.<ref name="Wang00"> | </ref> and polycyclic aromatic hydrocarbons.<ref name="Wang00"> | ||
| {{Cite journal | |
{{Cite journal |last=Wang |first=S. |title=A new carbonaceous material with large capacity and high efficiency for rechargeable Li-ion batteries |doi=10.1149/1.1393559 |journal=Journal of the Electrochemical Society |volume=147 |page=2498 |year=2000 |issue=7 |last2=Yata |first2=S. |last3=Nagano |first3=J. |last4=Okano |first4=Y. |last5=Kinoshita |first5=H. |last6=Kikuta |first6=H. |last7=Yamabe |first7=T. }}</ref> | ||
| The ] compendium of technology states: "previously, descriptions such as graphite layers, carbon layers, or carbon sheets have been used for the term graphene... it is incorrect to use for a single layer a term which includes the term graphite, which would imply a three-dimensional structure. The term graphene should be used only when the reactions, structural relations or other properties of individual layers are discussed."<ref name=iupac-gold-book>{{cite web |title=graphene layer |url=http://goldbook.iupac.org/G02683.html |work=IUPAC Gold Book |publisher=International Union of Pure and Applied Chemistry |accessdate=31 |
The ] compendium of technology states: "previously, descriptions such as graphite layers, carbon layers, or carbon sheets have been used for the term graphene... it is incorrect to use for a single layer a term which includes the term graphite, which would imply a three-dimensional structure. The term graphene should be used only when the reactions, structural relations or other properties of individual layers are discussed."<ref name=iupac-gold-book>{{cite web |title=graphene layer |url=http://goldbook.iupac.org/G02683.html |work=IUPAC Gold Book |publisher=International Union of Pure and Applied Chemistry |accessdate=2012-03-31 }}</ref> | ||
| Graphene can be considered an "infinite alternant" (only six-member carbon ring) ] (PAH). The largest known isolated PAH molecule consists of 222 atoms and is 10 ]s across.<!-- why is this relevant to graphene? --><ref>{{Cite journal | |
Graphene can be considered an "infinite alternant" (only six-member carbon ring) ] (PAH). The largest known isolated PAH molecule consists of 222 atoms and is 10 ]s across.<!-- why is this relevant to graphene? --><ref>{{Cite journal |last=Simpson |first=C. D. |title=Synthesis of a Giant 222 Carbon Graphite Sheet |doi=10.1002/1521-3765(20020315)8:6<1424::AID-CHEM1424>3.0.CO;2-Z |journal=Chemistry – A European Journal |volume=6 |page=1424 |year=2002 |issue=6 |last2=Brand |first2=J. Diedrich |last3=Berresheim |first3=Alexander J. |last4=Przybilla |first4=Laurence |last5=Räder |first5=Hans Joachim |last6=Müllen |first6=Klaus }}</ref> It has proven difficult to synthesize even slightly bigger molecules, and they still remain "a dream of many organic and polymer chemists".<ref name=2Dpolymers>{{Cite journal |last=Sakamoto |first=J. |last2=Van Heijst |first2=Jeroen |last3=Lukin |first3=Oleg |last4=Schlüter |first4=A. Dieter |title=Two-Dimensional Polymers: Just a Dream of Synthetic Chemists? |year=2009 |journal=Angew. Chem. Int. Ed. |pmid=19130514 |volume=48 |issue=16 |doi=10.1002/anie.200801863 |pages=1030–69 }}</ref> | ||
| A definition of "isolated or free-standing graphene" was proposed: "graphene is a single atomic plane of graphite, which – and this is essential – is sufficiently isolated from its environment to be considered free-standing."<ref name=Sciencerev09>{{Cite journal | |
A definition of "isolated or free-standing graphene" was proposed: "graphene is a single atomic plane of graphite, which – and this is essential – is sufficiently isolated from its environment to be considered free-standing."<ref name=Sciencerev09>{{Cite journal |last=Geim |first=A. |year=2009 |title=Graphene: Status and Prospects |journal=Science |pmid=19541989 |volume=324 |issue=5934 |doi=10.1126/science.1158877 |bibcode=2009Sci...324.1530G |pages=1530–4 |arxiv=0906.3799 }}</ref> This definition is narrower than the definition given above and refers to cleaved, transferred and suspended graphene monolayers.{{Citation needed|date=December 2011}} Other forms of graphene, such as graphene grown on various metals, can become free-standing if, for example, suspended or transferred to ] ({{chem|SiO|2}}) or ] (after its ] with hydrogen).<ref name=SiCplusH2>{{Cite journal |last=Riedl |first=C. |last2=Coletti |first2=C. |last3=Iwasaki |first3=T. |last4=Zakharov |first4=A.A. |last5=Starke |first5=U. |year=2009 |title=Quasi-Free-Standing Epitaxial Graphene on SiC Obtained by Hydrogen Intercalation |journal=Physical Review Letters |volume=103 |page=246804 |doi=10.1103/PhysRevLett.103.246804 |pmid=20366220 |bibcode=2009PhRvL.103x6804R |issue=24|arxiv=0911.1953 }}</ref> | ||
| == History == | == History == | ||
| In 1859 ] was aware of the highly ] structure of thermally reduced ].<ref> | In 1859 ] was aware of the highly ] structure of thermally reduced ].<ref>{{cite journal |last=Brodie |first=B. C. |year=1859 |title=On the Atomic Weight of Graphite |journal=] |volume=149 |issue= |pages=249–259 |bibcode=1859RSPT..149..249B |jstor=108699 }}</ref> | ||
| {{cite journal | |||
| | last1=Brodie |first1=B. C. | |||
| | year=1859 | |||
| | title=On the Atomic Weight of Graphite | |||
| | journal=] | |||
| | volume=149 |issue= |pages=249–259 | |||
| | bibcode=1859RSPT..149..249B | |||
| | jstor=108699 | |||
| }}</ref> | |||
| The structure of ] was solved in 1916.<ref>{{cite journal|year |
The structure of ] was solved in 1916.<ref>{{cite journal |year=1916 |title=Interferenz an regellos orientierten Teilchen im Röntgenlicht I |journal=Physikalische Zeitschrift |volume=17 |page=277 |last=Debije |first=P |last2=Scherrer |first2=P |authorlink1=Peter Debye }}</ref> by the related method of ],<ref>{{cite journal |last=Friedrich |first=W |year=1913 |title=Eine neue Interferenzerscheinung bei Röntgenstrahlen |journal=Physikalische Zeitschrift |volume=14 |page=317 }}</ref><ref>{{cite journal |last=Hull |first=AW |authorlink=Albert Hull |year=1917 |title=A New Method of X-ray Crystal Analysis |journal=Phys. Rev. |volume=10 |page=661 |doi=10.1103/PhysRev.10.661|issue=6 |bibcode=1917PhRv...10..661H }}</ref> It was studied in detail by V. Kohlschütter and P. Haenni in 1918, who also described the properties of ].<ref name=Kohlschuttler1918> | ||
| {{cite journal | {{cite journal | ||
| | |
|last=Kohlschütter |first=V. | ||
| | |
|last2=Haenni |first2=P. | ||
| | |
|year=1919 | ||
| | |
|title=Zur Kenntnis des Graphitischen Kohlenstoffs und der Graphitsäure | ||
| | |
|journal=] | ||
| | |
|volume=105 |issue=1 |pages=121–144 | ||
| | |
|doi=10.1002/zaac.19191050109 | ||
| }}</ref> Its structure was determined from single-crystal diffraction in 1924.<ref>{{cite journal| |
}}</ref> Its structure was determined from single-crystal diffraction in 1924.<ref>{{cite journal |last=Bernal |first=JD |authorlink=John Desmond Bernal |year=1924 |title=The Structure of Graphite |jstor=94336 |journal=Proc. R. Soc. Lond. |volume=A106 |issue=740 |pages=749–773 }}</ref><ref>{{cite journal |last=Hassel |first=O |last2=Mack |first2=H |year=1924 |title=Über die Kristallstruktur des Graphits |journal=Zeitschrift für Physik |volume=25 |page=317 |doi=10.1007/BF01327534 |bibcode=1924ZPhy...25..317H }}</ref> | ||
| The theory of graphene was first explored by ] in 1947 as a starting point for understanding the electronic properties of 3D graphite. The emergent massless Dirac equation was first pointed out by ] and David P. DeVincenzo and Eugene J. Mele.<ref name="devincenzo">{{Cite journal | |
The theory of graphene was first explored by ] in 1947 as a starting point for understanding the electronic properties of 3D graphite. The emergent massless Dirac equation was first pointed out by ] and David P. DeVincenzo and Eugene J. Mele.<ref name="devincenzo">{{Cite journal |last=DiVincenzo |first=D. P. |last2=Mele |first2=E. J. |title=Self-Consistent Effective Mass Theory for Intralayer Screening in Graphite Intercalation Compounds |doi=10.1103/PhysRevB.29.1685 |journal=Physical Review B |volume=295 |page=1685 |year=1984|bibcode=1984PhRvB..29.1685D |issue=4 }}</ref> Semenoff emphasized the occurrence in a magnetic field of an electronic ] precisely at the Dirac point. This level is responsible for the anomalous integer quantum Hall effect.<ref name="2dgasDiracFermions"/><ref name="Gusynin"/><ref name="Berry'sPhase"/> | ||
| The earliest TEM images of few-layer graphite were published by G. Ruess and F. Vogt in 1948.<ref name=RuessTEM> | The earliest TEM images of few-layer graphite were published by G. Ruess and F. Vogt in 1948.<ref name=RuessTEM> | ||
| {{cite journal |last=Ruess |first=G. |last2=Vogt |first2=F. |year=1948 |title=Höchstlamellarer Kohlenstoff aus Graphitoxyhydroxyd |journal=] | |||
| {{cite journal | |||
| |volume=78 |issue=3–4 |page=222 | |||
| | last1=Ruess |first1=G. | |||
| |doi=10.1007/BF01141527 | |||
| | last2=Vogt |first2=F. | |||
| }}</ref> Later, single graphene layers were also observed directly by electron microscopy.<ref name=Meyer07>{{Cite journal |last=Meyer |first=J. |last2=Geim |first2=A. K. |last3=Katsnelson |first3=M. I. |last4=Novoselov |first4=K. S. |last5=Booth |first5=T. J. |last6=Roth |first6=S. |title=The structure of suspended graphene sheets |journal=Nature |volume=446 |pages=60–63 |year=2007 |doi=10.1038/nature05545 |pmid=17330039 |issue=7131 |arxiv=cond-mat/0701379 |bibcode=2007Natur.446...60M }}</ref> Before 2004 intercalated graphite compounds were studied under a ] (TEM). Researchers occasionally observed thin graphitic flakes ("few-layer graphene") and possibly even individual layers. An early, detailed study on few-layer graphite dates to 1962.<ref name=GroxTEM> | |||
| | year=1948 | |||
| | title=Höchstlamellarer Kohlenstoff aus Graphitoxyhydroxyd | |||
| | journal=] | |||
| | volume=78 |issue=3–4 |page=222 | |||
| | doi=10.1007/BF01141527 | |||
| }}</ref> Later, single graphene layers were also observed directly by electron microscopy.<ref name=Meyer07>{{Cite journal | author = Meyer, J. ''et al.'' |title = The structure of suspended graphene sheets | journal = Nature | volume = 446 | pages = 60–63 | year =2007 |doi = 10.1038/nature05545 | pmid = 17330039 | issue = 7131 |arxiv = cond-mat/0701379 |bibcode = 2007Natur.446...60M | first2 = A. K. |last3 = Katsnelson | first3 = M. I. |last4 = Novoselov | first4 = K. S. |last5 = Booth | first5 = T. J. |last6 = Roth | first6 = S. |last2 = Geim }}</ref> Before 2004 intercalated graphite compounds were studied under a ] (TEM). Researchers occasionally observed thin graphitic flakes ("few-layer graphene") and possibly even individual layers. An early, detailed study on few-layer graphite dates to 1962.<ref name=GroxTEM> | |||
| {{cite book | {{cite book | ||
| |last=Boehm |first=H. P. |last2=Clauss |first2=A. |last3=Fischer |first3=G. |last4=Hofmann |first4=U. |year=1962 | |||
| | last1=Boehm |first1=H. P. | |||
| |chapter=Surface Properties of Extremely Thin Graphite Lamellae | |||
| | last2=Clauss |first2=A. | |||
| |url=http://graphenetimes.com/wp-content/uploads/1961/09/BoehmProcCarbon1962.pdf |format=PDF | |||
| | last3=Fischer |first3=G. | |||
| |booktitle=Proceedings of the Fifth Conference on Carbon | |||
| | last4=Hofmann |first4=U. | |||
| |publisher=] | |||
| | year=1962 | |||
| | chapter=Surface Properties of Extremely Thin Graphite Lamellae | |||
| | url=http://graphenetimes.com/wp-content/uploads/1961/09/BoehmProcCarbon1962.pdf | |||
| | booktitle=Proceedings of the Fifth Conference on Carbon | |||
| | publisher=] | |||
| }}</ref>{{#tag:ref|This paper reports graphitic flakes that give an additional contrast equivalent of down to ~0.4 nm or 3 atomic layers of amorphous carbon. This was the best possible resolution for 1960 TEMs. However, neither then nor today it is possible to argue how many layers were in those flakes. Now we know that the TEM contrast of graphene most strongly depends on focusing conditions.<ref name=Meyer07/> For example, it is impossible to distinguish between suspended monolayer and multilayer graphene by their TEM contrasts, and the only known way is to analyse relative intensities of various diffraction spots. The first reliable TEM observations of monolayers are probably given in refs. 24 and 26 of {{harvnb|Geim|Novoselov|2007}}}} | }}</ref>{{#tag:ref|This paper reports graphitic flakes that give an additional contrast equivalent of down to ~0.4 nm or 3 atomic layers of amorphous carbon. This was the best possible resolution for 1960 TEMs. However, neither then nor today it is possible to argue how many layers were in those flakes. Now we know that the TEM contrast of graphene most strongly depends on focusing conditions.<ref name=Meyer07/> For example, it is impossible to distinguish between suspended monolayer and multilayer graphene by their TEM contrasts, and the only known way is to analyse relative intensities of various diffraction spots. The first reliable TEM observations of monolayers are probably given in refs. 24 and 26 of {{harvnb|Geim|Novoselov|2007}}}} | ||
| Starting in the 1970s single layers of graphite were grown epitaxially on top of other materials.<ref name="Oshima97">{{Cite journal | |
Starting in the 1970s single layers of graphite were grown epitaxially on top of other materials.<ref name="Oshima97">{{Cite journal |last=Oshima |first=C. |last2=Nagashima |first2=A. |title=Ultra-thin epitaxial films of graphite and hexagonal boron nitride on solid surfaces |doi=10.1088/0953-8984/9/1/004 |journal=J. Phys.: Condens. Matter |volume=9 |page=1 |year=1997 |bibcode=1997JPCM....9....1O }}</ref> This "epitaxial graphene" consists of a single-atom-thick hexagonal lattice of ] carbon atoms, as in free-standing graphene. However, there is significant charge transfer from the substrate to the epitaxial graphene, and, in some cases, hybridization between the ]s of the substrate atoms and ] of graphene, which significantly alters the electronic structure of epitaxial graphene. | ||
| Single layers of graphite were also observed by ] within bulk materials, in particular inside soot obtained by chemical exfoliation. Efforts to make thin films of graphite by mechanical exfoliation started in 1990,<ref name=SciAm/> but nothing thinner than 50 to 100 layers was produced before 2004. | Single layers of graphite were also observed by ] within bulk materials, in particular inside soot obtained by chemical exfoliation. Efforts to make thin films of graphite by mechanical exfoliation started in 1990,<ref name=SciAm/> but nothing thinner than 50 to 100 layers was produced before 2004. | ||
| Line 99: | Line 80: | ||
| Initial attempts to make atomically thin graphitic films employed exfoliation techniques similar to the drawing method. Multilayer samples down to 10 nm in thickness were obtained.{{sfn|Geim|Novoselov|2007}} Old papers were unearthed<ref name=GroxTEM/> in which researchers tried to isolate graphene starting with intercalated compounds. These papers reported the observation of very thin graphitic fragments (possibly monolayers) by transmission electron microscopy. Neither of the earlier observations was sufficient to "spark the graphene gold rush", which awaited macroscopic samples of extracted atomic planes. | Initial attempts to make atomically thin graphitic films employed exfoliation techniques similar to the drawing method. Multilayer samples down to 10 nm in thickness were obtained.{{sfn|Geim|Novoselov|2007}} Old papers were unearthed<ref name=GroxTEM/> in which researchers tried to isolate graphene starting with intercalated compounds. These papers reported the observation of very thin graphitic fragments (possibly monolayers) by transmission electron microscopy. Neither of the earlier observations was sufficient to "spark the graphene gold rush", which awaited macroscopic samples of extracted atomic planes. | ||
| One of the very first patents pertaining to the production of graphene was filed in October, 2002 (US Pat. 7071258).<ref>. Patft.uspto.gov. Retrieved on 2014-01-12.</ref> Entitled, "Nano-scaled Graphene Plates", this patent detailed one of the very first large scale graphene production processes. Two years later, in 2004 ] and ] at University of Manchester extracted single-atom-thick crystallites from bulk graphite.<ref name="Nov 04"/> They pulled graphene layers from graphite and transferred them onto thin {{chem|SiO|2}} on a silicon wafer in a process called either micromechanical cleavage or the ] technique. The {{chem|SiO|2}} electrically isolated the graphene and weakly interacted with it, providing nearly charge-neutral graphene layers. The silicon beneath the {{chem|SiO|2}} could be used as a "back gate" electrode to vary the charge density in the graphene over a wide range. They may not have been the first to use this technique—{{ |
One of the very first patents pertaining to the production of graphene was filed in October, 2002 (US Pat. 7071258).<ref>. Patft.uspto.gov. Retrieved on 2014-01-12.</ref> Entitled, "Nano-scaled Graphene Plates", this patent detailed one of the very first large scale graphene production processes. Two years later, in 2004 ] and ] at University of Manchester extracted single-atom-thick crystallites from bulk graphite.<ref name="Nov 04"/> They pulled graphene layers from graphite and transferred them onto thin {{chem|SiO|2}} on a silicon wafer in a process called either micromechanical cleavage or the ] technique. The {{chem|SiO|2}} electrically isolated the graphene and weakly interacted with it, providing nearly charge-neutral graphene layers. The silicon beneath the {{chem|SiO|2}} could be used as a "back gate" electrode to vary the charge density in the graphene over a wide range. They may not have been the first to use this technique— {{patent|US|6667100}}, filed in 2002, describes how to process commercially available flexible expanded graphite to achieve a graphite thickness of 0.01 thousandth of an inch. The key to success was high-throughput visual recognition of graphene on a properly chosen substrate, which provides a small but noticeable optical contrast. | ||
| The cleavage technique led directly to the first observation of the ] in graphene,<ref name="2dgasDiracFermions"/><ref name="Berry'sPhase"/> which provided direct evidence of graphene's theoretically predicted ] of massless ]s. The effect was reported soon after by ] and Yuanbo Zhang in 2005. These experiments started after the researchers observed colleagues who were looking for the quantum Hall effect<ref>{{cite journal |last=Kopelevich |
The cleavage technique led directly to the first observation of the ] in graphene,<ref name="2dgasDiracFermions"/><ref name="Berry'sPhase"/> which provided direct evidence of graphene's theoretically predicted ] of massless ]s. The effect was reported soon after by ] and Yuanbo Zhang in 2005. These experiments started after the researchers observed colleagues who were looking for the quantum Hall effect<ref>{{cite journal |last=Kopelevich |first=Y. |last2=Torres |first2=J. |last3=Da Silva |first3=R. |last4=Mrowka |first4=F. |last5=Kempa |first5=H. |last6=Esquinazi |first6=P. |title=Reentrant Metallic Behavior of Graphite in the Quantum Limit |journal=Physical Review Letters |year=2003 |volume=90|page=156402 |doi=10.1103/PhysRevLett.90.156402 |issue=15 |pmid=12732058|arxiv=cond-mat/0209406 |bibcode=2003PhRvL..90o6402K }}</ref> and Dirac fermions<ref>{{cite journal |first=Igor A. |last=Luk’yanchuk |first2=Yakov |last2=Kopelevich |title=Phase Analysis of Quantum Oscillations in Graphite |journal=Physical Review Letters |year=2004 |volume=93|page=166402 |doi=10.1103/PhysRevLett.93.166402 |issue=16 |pmid=15525015 |arxiv=cond-mat/0402058 |bibcode=2004PhRvL..93p6402L }}</ref> in bulk graphite. | ||
| Even though graphene on nickel and on silicon carbide have both existed in the laboratory for decades, graphene mechanically exfoliated on {{chem|SiO|2}} provided the first proof of the Dirac fermion nature of electrons.{{Citation needed|date=September 2010}} | Even though graphene on nickel and on silicon carbide have both existed in the laboratory for decades, graphene mechanically exfoliated on {{chem|SiO|2}} provided the first proof of the Dirac fermion nature of electrons.{{Citation needed|date=September 2010}} | ||
| ] | ] | ||
| Geim and |
Geim and Novoselov received several awards for their pioneering research on graphene, notably the 2010 ].<ref>{{cite web |url=http://physicsworld.com/cws/article/news/43939 |title=Graphene pioneers bag Nobel prize |publisher=], UK |date=5 October 2010 }}</ref> | ||
| == Properties == | == Properties == | ||
| Line 112: | Line 93: | ||
| === Structure === | === Structure === | ||
| The ] of isolated, single-layer graphene was studied by ] (TEM) on sheets of graphene suspended between bars of a metallic grid.<ref name=Meyer07/> Electron diffraction patterns showed the expected honeycomb lattice. Suspended graphene also showed "rippling" of the flat sheet, with amplitude of about one nanometer. These ripples may be intrinsic to the material as a result of the instability of two-dimensional crystals,{{sfn|Geim|Novoselov|2007}}<ref name="Carlsson">{{Cite journal | |
The ] of isolated, single-layer graphene was studied by ] (TEM) on sheets of graphene suspended between bars of a metallic grid.<ref name=Meyer07/> Electron diffraction patterns showed the expected honeycomb lattice. Suspended graphene also showed "rippling" of the flat sheet, with amplitude of about one nanometer. These ripples may be intrinsic to the material as a result of the instability of two-dimensional crystals,{{sfn|Geim|Novoselov|2007}}<ref name="Carlsson">{{Cite journal |last=Carlsson |first=J. M. |title=Graphene: Buckle or break |doi=10.1038/nmat2051 |journal=Nature Materials |volume=6 |year=2007 |pmid=17972931 |issue=11 |bibcode=2007NatMa...6..801C |pages=801–2 }}</ref><ref name="Fasolino">{{Cite journal |last=Fasolino |first=A. |last2=Los |first2=J. H. |last3=Katsnelson |first3=M. I. |title=Intrinsic ripples in graphene |doi=10.1038/nmat2011 |journal=Nature Materials |volume=6 |year=2007 |pmid=17891144 |issue=11 |bibcode=2007NatMa...6..858F |pages=858–61 |arxiv=0704.1793 }}</ref> or may originate from the ubiquitous dirt seen in all TEM images of graphene. Atomic resolution real-space images of isolated, single-layer graphene on {{chem|SiO|2}} substrates are available<ref name=Ishigami07>{{Cite journal |last=Ishigami |first=Masa |author2=et al. |year=2007 |volume=7 |issue=6 |pages=1643–1648 |title=Atomic Structure of Graphene on SiO<sub>2</sub> |journal=Nano Lett |doi=10.1021/nl070613a |pmid=17497819 |bibcode=2007NanoL...7.1643I }}</ref><ref name="Stolyarova">{{Cite journal |last=Stolyarova |first=Elena |author2=et al. |year=2007 |volume=104 |pages=9209–9212 |title=High-resolution scanning tunneling microscopy imaging of mesoscopic graphene sheets on an insulating surface |journal=Proceedings of the National Academy of Sciences |doi=10.1073/pnas.0703337104 |pmid=17517635 |issue=22 |pmc=1874226 |bibcode=2007PNAS..104.9209S |arxiv=0705.0833 }}</ref> via ]. ] residue, which must be removed to obtain atomic-resolution images, may be the "]s" observed in TEM images, and may explain the observed rippling. Rippling on {{chem|SiO|2}} is caused by conformation of graphene to the underlying {{chem|SiO|2}}, and is not intrinsic.<ref name=Ishigami07/> | ||
| Graphene sheets in solid form usually show evidence in diffraction for graphite's (002) layering. This is true of some single-walled nanostructures.<ref>{{Cite journal | |
Graphene sheets in solid form usually show evidence in diffraction for graphite's (002) layering. This is true of some single-walled nanostructures.<ref>{{Cite journal |last=Kasuya |first=D. |last2=Yudasaka |first2=M. |last3=Takahashi |first3=K. |last4=Kokai |first4=F. |last5=Iijima |first5=S. |title=Selective Production of Single-Wall Carbon Nanohorn Aggregates and Their Formation Mechanism |doi=10.1021/jp020387n |journal=J. Phys. Chem. B |volume=106 |year=2002 |page=4947 |issue=19 }}</ref> However, unlayered graphene with only (hk0) rings has been found in the core of ] graphite onions.<ref>{{Cite journal |author=Bernatowicz |author2=T. J. <!-- check this --> |last3=Gibbons |first3=Patrick C. |last4=Lodders |first4=Katharina |last5=Fegley |first5=Bruce |last6=Amari |first6=Sachiko |last7=Lewis |first7=Roy S. |display-authors=2 |year=1996 |title=Constraints on stellar grain formation from presolar graphite in the Murchison meteorite |journal=Astrophysical Journal |volume=472 |pages=760–782 |doi=10.1086/178105 |bibcode=1996ApJ...472..760B |issue=2 }}</ref> TEM studies show faceting at defects in flat graphene sheets<ref>{{Cite journal |last=Fraundorf |first=P. |last2=Wackenhut |first2=M. |year=2002 |title=The core structure of presolar graphite onions |journal=Astrophysical Journal Letters |volume=578 |page=L153–156 |arxiv=astro-ph/0110585 |doi=10.1086/344633 |bibcode=2002ApJ...578L.153F |issue=2 }}</ref> and suggest a role for two-dimensional crystallization from a melt. | ||
| Graphene can self-repair holes in its sheets, when exposed to molecules containing carbon, such as ]s. Bombarded with pure carbon atoms, the atoms perfectly align into ]s, completely filling the holes.<ref name=Manchester>{{Cite journal |year |
Graphene can self-repair holes in its sheets, when exposed to molecules containing carbon, such as ]s. Bombarded with pure carbon atoms, the atoms perfectly align into ]s, completely filling the holes.<ref name=Manchester>{{Cite journal |year=2012 |doi=10.1021/nl300985q |title=Graphene re-knits its holes |journal=Mesoscale and Nanoscale Physics |arxiv=1207.1487v1 |first=Recep |last=Zan |first2=Quentin M. |last2=Ramasse |first3=Ursel |last3=Bangert |first4=Konstantin S. |last4=Novoselov |volume=12 |issue=8 |page=3936|bibcode=2012NanoL..12.3936Z |last2=Ramasse |last3=Bangert |last4=Novoselov }}</ref><ref>Puiu, Tibi (July 12, 2012) . zmescience.com</ref> | ||
| === Chemical === | === Chemical === | ||
| Graphene is the only form of carbon (and generally all solid materials) in which each single atom is in exposure for chemical reaction from two sides (due to the 2D structure). It is known that carbon atoms at the edge of graphene sheets have special chemical reactivity, and graphene has the highest ratio of edgy carbons (in comparison with similar materials such as carbon nanotubes). In addition, various types of defects within the sheet, which are very common, increase the chemical reactivity.<ref name="Denis">{{Cite journal | |
Graphene is the only form of carbon (and generally all solid materials) in which each single atom is in exposure for chemical reaction from two sides (due to the 2D structure). It is known that carbon atoms at the edge of graphene sheets have special chemical reactivity, and graphene has the highest ratio of edgy carbons (in comparison with similar materials such as carbon nanotubes). In addition, various types of defects within the sheet, which are very common, increase the chemical reactivity.<ref name="Denis">{{Cite journal |last=Denis |first=P. A. |last2=Iribarne |first2=F. |title=Comparative Study of Defect Reactivity in Graphene |doi=10.1021/jp4061945 |journal=Journal of Physical Chemistry C |volume=117 |page=19048 |year=2013 |issue=37 }}</ref> The onset temperature of reaction between the basal plane of single-layer graphene and oxygen gas is below 260 °C <ref name="Yamada3">{{Cite journal |last=Yamada |first=Y. |last2=Murota |first2=K |last3=Fujita |first3=R |last4=Kim |first4=J |author5=et al. |title=Subnanometer vacancy defects introduced on graphene by oxygen gas |doi=10.1021/ja4117268 |journal=Journal of American Chemical Society |volume=136 |issue=6 |pages=2232 |year=2014 }}</ref> and the graphene burns at very low temperature (e.g., 350 °C).<ref name="Eftekhari">{{Cite journal |last=Eftekhari |first=A. |last2=Jafarkhani |first2=P. |title=Curly Graphene with Specious Interlayers Displaying Superior Capacity for Hydrogen Storage |doi=10.1021/jp410044v |journal=Journal of Physical Chemistry C |volume=117 |page=25845 |year=2013 |issue=48 }}</ref> In fact, graphene is chemically the most reactive form of carbon, owing to the lateral availability of carbon atoms. | ||
| Graphene is commonly modified with oxygen- and nitrogen-containing functional groups and analyzed by infrared spectroscopy and X-ray photoelectron spectroscopy. But, determination of structures of graphene with oxygen-<ref name="Yamada">{{Cite journal | |
Graphene is commonly modified with oxygen- and nitrogen-containing functional groups and analyzed by infrared spectroscopy and X-ray photoelectron spectroscopy. But, determination of structures of graphene with oxygen-<ref name="Yamada">{{Cite journal |last=Yamada |first=Y. |last2=Yasuda |first2=H. |last3=Murota |first3=K. |last4=Nakamura |first4=M. |last5=Sodesawa |first5=T. |last6=Sato |first6=S. |title=Analysis of heat-treated graphite oxide by X-ray photoelectron spectroscopy |doi=10.1007/s10853-013-7630-0 |journal=Journal of Material Science |volume=48 |page=8171 |year=2013 |issue=23 }}</ref> and nitrogen-<ref name="Yamada2">{{Cite journal |last=Yamada |first=Y. |last2=Kim |first2=J. |last3=Murota |first3=K. |last4=Matsuo |first4=S. |last5=Sato |first5=S. |title=Nitrogen-containing graphene analyzed by X-ray photoelectron spectroscopy |doi=10.1016/j.carbon.2013.12.061 |journal=Carbon |volume=70 |pages=59 |year=2014 }}</ref> containing functional groups is a difficult task unless the structures are well controlled. | ||
| In 2013, ] physicists reported that sheets of Graphene one atom thick are a hundred times more chemically reactive than thicker sheets.<ref>{{cite web|url=http://phys.org/news/2013-02-thinnest-graphene-sheets-react-strongly.html|title=Thinnest graphene sheets react strongly with hydrogen atoms; thicker sheets are relatively unaffected|publisher=Phys.org|date=1 February 2013 |
In 2013, ] physicists reported that sheets of Graphene one atom thick are a hundred times more chemically reactive than thicker sheets.<ref>{{cite web |url=http://phys.org/news/2013-02-thinnest-graphene-sheets-react-strongly.html |title=Thinnest graphene sheets react strongly with hydrogen atoms; thicker sheets are relatively unaffected |publisher=Phys.org |date=1 February 2013 }}</ref> | ||
| === Physical === | === Physical === | ||
| The ] length in graphene is about 0.142 ]s.<ref>{{cite arXiv |eprint=0804.4086 | |
The ] length in graphene is about 0.142 ]s.<ref>{{cite arXiv |eprint=0804.4086 |first=Raji |last=Heyrovska|title=Atomic Structures of Graphene, Benzene and Methane with Bond Lengths as Sums of the Single, Double and Resonance Bond Radii of Carbon |class=physics.gen-ph |year=2008 }}</ref> Graphene sheets stack to form graphite with an interplanar spacing of 0.335 nm. | ||
| === Electronic === | === Electronic === | ||
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| ] band structure for armchair orientation. Tightbinding calculations show that armchair orientation can be semiconducting or metallic depending on width (chirality).]] | ] band structure for armchair orientation. Tightbinding calculations show that armchair orientation can be semiconducting or metallic depending on width (chirality).]] | ||
| Graphene differs from most three-dimensional materials. Intrinsic graphene is a ] or zero-gap ]. Understanding the electronic structure of graphene is the starting point for finding the band structure of graphite. The energy-momentum relation (]) is linear for low energies near the six corners of the two-dimensional hexagonal ], leading to zero ] for electrons and ].<ref name="E-Phonon">{{Cite book | |
Graphene differs from most three-dimensional materials. Intrinsic graphene is a ] or zero-gap ]. Understanding the electronic structure of graphene is the starting point for finding the band structure of graphite. The energy-momentum relation (]) is linear for low energies near the six corners of the two-dimensional hexagonal ], leading to zero ] for electrons and ].<ref name="E-Phonon">{{Cite book |last=Charlier |first=J.-C. |last2=Eklund |first2=P.C.|last3=Zhu|first3=J. |last4=Ferrari |first4=A.C. |chapter=Electron and Phonon Properties of Graphene: Their Relationship with Carbon Nanotubes |title=from Carbon Nanotubes: Advanced Topics in the Synthesis, Structure, Properties and Applications, Ed. A. Jorio, G. Dresselhaus, and M.S. Dresselhaus |location=Berlin/Heidelberg |publisher=Springer-Verlag |year=2008 }}</ref> Due to this linear (or "]") dispersion relation at low energies, electrons and holes near these six points, two of which are inequivalent, behave like ] particles described by the ] for spin-1/2 particles.<ref name="Semenoff">{{Cite journal |last=Semenoff |first=G. W. |title=Condensed-Matter Simulation of a Three-Dimensional Anomaly |doi=10.1103/PhysRevLett.53.2449 |journal=Physical Review Letters |volume=53 |page=2449 |year=1984 |bibcode=1984PhRvL..53.2449S |issue=26 }}</ref><ref name=CBE>{{Cite journal |last=Avouris |first=P. |last2=Chen |first2=Z. |last3=Perebeinos |first3=V. |title=Carbon-based electronics |doi=10.1038/nnano.2007.300 |journal=Nature Nanotechnology |volume=2 |year=2007 |pmid=18654384 |issue=10 |bibcode=2007NatNa...2..605A |pages=605–15 }}</ref> Hence, the electrons and holes are called Dirac ] and the six corners of the Brillouin zone are called the Dirac points.<ref name="Semenoff"/> The equation describing the electrons' linear dispersion relation is <math>E=\hbar v_F\sqrt{k_x^2+k_y^2}</math>; where the ] ''v<sub>F</sub>'' ~ {{val|e=6|u=m/s}}, and the ] ''k'' is measured from the Dirac points (the zero of energy is chosen here to coincide with the Dirac points).<ref name=CBE/> | ||
| Electrical resistance in 40-nanometer-wide ]s of epitaxially-applied graphene changes in discrete steps following ] principles. Graphene nanoribbons can act more like ]s or ]s, allowing electrons to flow smoothly along the material's edges. In conductors such as copper, resistance increases in proportion to the length as electrons encounter more and more impurities while moving through the conductor. Electrons travel ballistically, similar to those observed in cylindrical ]s, exceeding theoretical conductance predictions for graphene by a factor of 10. Electrons in the nanoribbons can move tens or hundreds of microns without scattering.<ref name=k1402></ref><ref>{{cite doi|10.1038/nature12952}}</ref> | Electrical resistance in 40-nanometer-wide ]s of epitaxially-applied graphene changes in discrete steps following ] principles. Graphene nanoribbons can act more like ]s or ]s, allowing electrons to flow smoothly along the material's edges. In conductors such as copper, resistance increases in proportion to the length as electrons encounter more and more impurities while moving through the conductor. Electrons travel ballistically, similar to those observed in cylindrical ]s, exceeding theoretical conductance predictions for graphene by a factor of 10. Electrons in the nanoribbons can move tens or hundreds of microns without scattering.<ref name=k1402></ref><ref>{{cite doi|10.1038/nature12952 }}</ref> | ||
| The measured graphene nanoribbons were approximately 40 nanometers wide that had been grown on the edges of three-dimensional structures etched into ] wafers. When the wafers are heated to approximately {{convert|1000|C|F}}, silicon is preferentially driven off along the edges, forming graphene nanoribbons whose structure is determined by the pattern of the three-dimensional surface.<ref name=k1402/> | The measured graphene nanoribbons were approximately 40 nanometers wide that had been grown on the edges of three-dimensional structures etched into ] wafers. When the wafers are heated to approximately {{convert|1000|C|F}}, silicon is preferentially driven off along the edges, forming graphene nanoribbons whose structure is determined by the pattern of the three-dimensional surface.<ref name=k1402/> | ||
| The nanoribbons have perfectly smooth edges, annealed by the fabrication process. Electrons on the edge flow more like photons in ], helping them avoid scattering. Ballistic conductance extended for up to 16 microns. Electron mobility measurements surpassing one million correspond to a sheet resistance of one ohm per square— two orders of magnitude lower than what is observed in two-dimensional graphene and one tenth of theoretical predictions.<ref name=k1402/> | The nanoribbons have perfectly smooth edges, annealed by the fabrication process. Electrons on the edge flow more like photons in ], helping them avoid scattering. Ballistic conductance extended for up to 16 microns. Electron mobility measurements surpassing one million correspond to a ] of one ohm per square— two orders of magnitude lower than what is observed in two-dimensional graphene and one tenth of theoretical predictions.<ref name=k1402/> | ||
| Transport is dominated by two modes. One is ballistic and temperature independent; while the other is thermally activated. Transport is protected from back-scattering, possibly reflecting ground-state properties of neutral graphene. At room temperature, the resistance of both modes is found to increase abruptly at a particular length—the ballistic mode at 16 micrometres and the other at 160 nanometres.<ref name=k1402/> | Transport is dominated by two modes. One is ballistic and temperature independent; while the other is thermally activated. Transport is protected from back-scattering, possibly reflecting ground-state properties of neutral graphene. At room temperature, the resistance of both modes is found to increase abruptly at a particular length—the ballistic mode at 16 micrometres and the other at 160 nanometres.<ref name=k1402/> | ||
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| === "Massive" electrons === | === "Massive" electrons === | ||
| Graphene's unit cell has two identical carbon atoms and two zero-energy states: one in which the electron resides on atom A, the other in which the electron resides on atom B. Both states exist at exactly zero energy. However, if the two atoms in the unit cell are not identical, the situation changes. Hunt et al. show that placing hBN in contact with graphene can alter the potential felt at atom A versus atom B enough that the electrons develop a mass and accompanying band gap of about 30 meV.<ref name=sci1306>{{cite doi|10.1126/science.1240317}}</ref> | Graphene's unit cell has two identical carbon atoms and two zero-energy states: one in which the electron resides on atom A, the other in which the electron resides on atom B. Both states exist at exactly zero energy. However, if the two atoms in the unit cell are not identical, the situation changes. Hunt et al. show that placing hBN in contact with graphene can alter the potential felt at atom A versus atom B enough that the electrons develop a mass and accompanying band gap of about 30 meV.<ref name=sci1306>{{cite doi|10.1126/science.1240317 }}</ref> | ||
| The mass can be positive or negative. An arrangement that slightly raises the energy of an electron on atom A relative to atom B gives it a positive mass, while an arrangement that raises the energy of atom B produces a negative electron mass. The two versions behave alike and are indistinguishable via ]. An electron traveling from a positive-mass region to a negative-mass region must cross an intermediate region where its mass once again becomes zero. This region is gapless and therefore metallic. Metallic modes bounding semiconducting regions of opposite-sign mass is a hallmark of a topological phase and display much the same physics as topological insulators.<ref name=sci1306/> | The mass can be positive or negative. An arrangement that slightly raises the energy of an electron on atom A relative to atom B gives it a positive mass, while an arrangement that raises the energy of atom B produces a negative electron mass. The two versions behave alike and are indistinguishable via ]. An electron traveling from a positive-mass region to a negative-mass region must cross an intermediate region where its mass once again becomes zero. This region is gapless and therefore metallic. Metallic modes bounding semiconducting regions of opposite-sign mass is a hallmark of a topological phase and display much the same physics as topological insulators.<ref name=sci1306/> | ||
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| ==== Electron transport ==== | ==== Electron transport ==== | ||
| Experimental results from transport measurements show that graphene has a remarkably high ] at room temperature, with reported values in excess of {{val|fmt=commas|15000|u=cm<sup>2</sup>·V<sup>−1</sup>·s<sup>−1</sup>}}.{{sfn|Geim|Novoselov|2007}} Additionally, the symmetry of the experimentally measured conductance indicates that hole and electron mobilities should be nearly the same.<ref name="E-Phonon"/> The mobility is nearly independent of temperature between {{val|10|u=K}} and {{val|100|u=K}},<ref name="2dgasDiracFermions">{{Cite journal | |
Experimental results from transport measurements show that graphene has a remarkably high ] at room temperature, with reported values in excess of {{val|fmt=commas|15000|u=cm<sup>2</sup>·V<sup>−1</sup>·s<sup>−1</sup>}}.{{sfn|Geim|Novoselov|2007}} Additionally, the symmetry of the experimentally measured conductance indicates that hole and electron mobilities should be nearly the same.<ref name="E-Phonon"/> The mobility is nearly independent of temperature between {{val|10|u=K}} and {{val|100|u=K}},<ref name="2dgasDiracFermions">{{Cite journal |last=Novoselov |first=K. S. |title=Two-dimensional gas of massless Dirac fermions in graphene |doi=10.1038/nature04233 |journal=Nature |volume=438 |pages=197–200 |year=2005 |pmid=16281030 |issue=7065 |arxiv=cond-mat/0509330 |bibcode=2005Natur.438..197N |last2=Geim |first2=A. K. |last3=Morozov |first3=S. V. |last4=Jiang |first4=D. |last5=Katsnelson |first5=M. I. |last6=Grigorieva |first6=I. V. |last7=Dubonos |first7=S. V. |last8=Firsov |first8=A. A. }}</ref><ref name="GiantMobility">{{Cite journal |last=Morozov |first=S.V. |title=Giant Intrinsic Carrier Mobilities in Graphene and Its Bilayer |doi=10.1103/PhysRevLett.100.016602 |journal=Physical Review Letters |volume=100 |page=016602 |year=2008 |pmid=18232798 |bibcode=2008PhRvL.100a6602M |issue=1 |last2=Novoselov |first2=K. |last3=Katsnelson |first3=M. |last4=Schedin |first4=F. |last5=Elias |first5=D. |last6=Jaszczak |first6=J. |last7=Geim |first7=A. |arxiv=0710.5304 }}</ref><ref name=E-ph>{{Cite journal |last=Chen |first=J. H. |title=Intrinsic and Extrinsic Performance Limits of Graphene Devices on SiO<sub>2</sub> |doi=10.1038/nnano.2008.58 |journal=Nature Nanotechnology |volume=3 |year=2008 |pmid=18654504 |issue=4 |pages=206–9 |last2=Jang |first2=Chaun |last3=Xiao |first3=Shudong |last4=Ishigami |first4=Masa |last5=Fuhrer |first5=Michael S. }}</ref> which implies that the dominant scattering mechanism is ]. Scattering by the acoustic ]s of graphene intrinsically limits room temperature mobility to {{val|fmt=commas|200000|u=cm<sup>2</sup>·V<sup>−1</sup>·s<sup>−1</sup>}} at a carrier density of {{val|e=12|u=cm<sup>−2</sup>}}.<ref name=E-ph/><ref name="GrapheneMC">{{Cite journal |last=Akturk |first=A. |last2=Goldsman |first2=N. |title=Electron transport and full-band electron–phonon interactions in graphene |doi=10.1063/1.2890147 |journal=Journal of Applied Physics |volume=103 |page=053702 |year=2008 |bibcode=2008JAP...103e3702A |issue=5 }}</ref> The corresponding ] of the graphene sheet would be {{val|e=-6|u=Ω·cm}}. This is less than the resistivity of ], the lowest known at room temperature.<ref name="UMDnews">. Newsdesk.umd.edu (2008-03-24). Retrieved on 2014-01-12.</ref> However, for graphene on {{chem|SiO|2}} substrates, scattering of electrons by optical phonons of the substrate is a larger effect at room temperature than scattering by graphene’s own phonons. This limits mobility to {{val|fmt=commas|40000|u=cm<sup>2</sup>·V<sup>−1</sup>·s<sup>−1</sup>}}.<ref name=E-ph/> | ||
| Despite zero carrier density near the Dirac points, graphene exhibits a minimum ] on the order of <math>4e^2/h</math>. The origin of this minimum conductivity is still unclear. However, rippling of the graphene sheet or ionized impurities in the {{chem|SiO|2}} substrate may lead to local puddles of carriers that allow conduction.<ref name="E-Phonon"/> Several theories suggest that the minimum conductivity should be <math>4e^2/{(\pi}h)</math>; however, most measurements are of order <math>4e^2/h</math> or greater{{sfn|Geim|Novoselov|2007}} and depend on impurity concentration.<ref name=K>{{Cite journal | |
Despite zero carrier density near the Dirac points, graphene exhibits a minimum ] on the order of <math>4e^2/h</math>. The origin of this minimum conductivity is still unclear. However, rippling of the graphene sheet or ionized impurities in the {{chem|SiO|2}} substrate may lead to local puddles of carriers that allow conduction.<ref name="E-Phonon"/> Several theories suggest that the minimum conductivity should be <math>4e^2/{(\pi}h)</math>; however, most measurements are of order <math>4e^2/h</math> or greater{{sfn|Geim|Novoselov|2007}} and depend on impurity concentration.<ref name=K>{{Cite journal |last=Chen |first=J. H. |title=Charged Impurity Scattering in Graphene |doi=10.1038/nphys935 |journal=Nature Physics |volume=4 |pages=377–381 |year=2008 |bibcode=2008NatPh...4..377C |issue=5 |last2=Jang |first2=C. |last3=Adam |first3=S. |last4=Fuhrer |first4=M. S. |last5=Williams |first5=E. D. |last6=Ishigami |first6=M. |arxiv=0708.2408 }}</ref> | ||
| Graphene doped with various gaseous species (both acceptors and donors) can be returned to an undoped state by gentle heating in vacuum.<ref name=K/><ref name="ChemDoping">{{Cite journal | |
Graphene doped with various gaseous species (both acceptors and donors) can be returned to an undoped state by gentle heating in vacuum.<ref name="K" /><ref name="ChemDoping">{{Cite journal |last=Schedin |first=F. |title=Detection of individual gas molecules adsorbed on graphene |doi=10.1038/nmat1967 |journal=Nature Materials |volume=6 |pages=652–655 |year=2007 |pmid=17660825 |issue=9 |bibcode=2007NatMa...6..652S |last2=Geim |first2=A. K. |last3=Morozov |first3=S. V. |last4=Hill |first4=E. W. |last5=Blake |first5=P. |last6=Katsnelson |first6=M. I. |last7=Novoselov |first7=K. S. }}</ref> Even for ] concentrations in excess of 10<sup>12</sup> cm<sup>−2</sup> carrier mobility exhibits no observable change.<ref name="ChemDoping"/> Graphene doped with ] in ] at low temperature can reduce mobility 20-fold.<ref name="K" /><ref name="GrapheneCharge">{{Cite journal |last=Adam |first=S. |title=A self-consistent theory for graphene transport |journal=Proc. Nat. Acad. Sci. USA |volume=104 |arxiv=0705.1540 |year=2007 |doi=10.1073/pnas.0704772104 |pmid=18003926 |issue=47 |pmc=2141788 |bibcode=2007PNAS..10418392A |pages=18392–7 |last2=Hwang |first2=E. H. |last3=Galitski |first3=V. M. |last4=Das Sarma |first4=S. }}</ref> The mobility reduction is reversible on heating the graphene to remove the potassium. | ||
| Due to graphene's two dimensions, charge fractionalization (where the apparent charge of individual pseudoparticles in low-dimensional systems is less than a single quantum<ref>{{Cite journal | |
Due to graphene's two dimensions, charge fractionalization (where the apparent charge of individual pseudoparticles in low-dimensional systems is less than a single quantum<ref>{{Cite journal |first=Hadar |last=Steinberg |first2=Gilad |last2=Barak |first3=Amir |last3=Yacoby |author4=et al. |title=Charge fractionalization in quantum wires (Letter) |journal=Nature Physics |volume=4 |issue=2 |year=2008 |pages=116–119 |doi=10.1038/nphys810 |bibcode=2008NatPh...4..116S |arxiv=0803.0744 }}</ref>) is thought to occur. It may therefore be a suitable material for constructing ]s<ref>{{Cite journal |arxiv=1003.4590 |title=Dirac four-potential tunings-based quantum transistor utilizing the Lorentz force |first=Agung |last=Trisetyarso |journal=Quantum Information & Computation |url=http://dl.acm.org/citation.cfm?id=2481569.2481576 |volume=12 |year=2012 |page=989 |bibcode=2010arXiv1003.4590T |issue=11–12 }}</ref> using ]ic circuits.<ref>{{Cite journal |arxiv=0812.1116 |title=Manifestations of topological effects in graphene |first=Jiannis K. |last=Pachos |journal=Contemporary Physics |doi=10.1080/00107510802650507 |volume=50 |year=2009 |page=375 |bibcode=2009ConPh..50..375P |issue=2 }}<br/>, M. Franz, University of British Columbia, January 5, 2008</ref> | ||
| === Optical === | === Optical === | ||
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| ] above}}Photograph of graphene in transmitted light. This one-atom-thick crystal can be seen with the naked eye because it absorbs approximately 2.3% of white light.]] | ] above}}Photograph of graphene in transmitted light. This one-atom-thick crystal can be seen with the naked eye because it absorbs approximately 2.3% of white light.]] | ||
| Graphene's unique optical properties produce an unexpectedly high ] for an atomic monolayer in vacuum, absorbing ''πα'' ≈ 2.3% of white ], where ''α'' is the ].<ref>{{Cite journal |title=Universal infrared conductance of graphite | |
Graphene's unique optical properties produce an unexpectedly high ] for an atomic monolayer in vacuum, absorbing ''πα'' ≈ 2.3% of white ], where ''α'' is the ].<ref>{{Cite journal |title=Universal infrared conductance of graphite |first=A. B. |last=Kuzmenko |first2=E. |last2=Van Heumen |first3=F. |last3=Carbone |first4=D. |last4=Van Der Marel |journal=Physical Review Letters |volume=100 |page=117401 |doi=10.1103/PhysRevLett.100.117401 |year=2008 |pmid=18517825 |issue=11 |bibcode=2008PhRvL.100k7401K |arxiv=0712.0835 }}</ref> This is a consequence of the "unusual low-energy electronic structure of monolayer graphene that features electron and hole ] meeting each other at the ]... is qualitatively different from more common ]s".<ref>{{Cite journal |title=Fine Structure Constant Defines Visual Transparency of Graphene |url=http://onnes.ph.man.ac.uk/nano/Publications/Science_2008fsc.pdf |format=PDF |last=Nair |first=R. R. |journal=] |year=2008 |doi=10.1126/science.1156965 |volume=320 |page=1308 |pmid=18388259 |issue=5881 |bibcode=2008Sci...320.1308N |last2=Blake |first2=P. |last3=Grigorenko |first3=A. N. |last4=Novoselov |first4=K. S. |last5=Booth |first5=T. J. |last6=Stauber |first6=T. |last7=Peres |first7=N. M. R. |last8=Geim |first8=A. K. }} </ref> Based on the Slonczewski–Weiss–McClure (SWMcC) band model of graphite, the interatomic distance, hopping value and frequency cancel when optical conductance is calculated using ] in the thin-film limit. | ||
| Although confirmed experimentally, the measurement is not precise enough to improve on other techniques for determining the ].<ref>{{Cite news |title=Graphene Gazing Gives Glimpse Of Foundations Of Universe |url=http://www.sciencedaily.com/releases/2008/04/080403140918.htm |publisher=ScienceDaily |date= |
Although confirmed experimentally, the measurement is not precise enough to improve on other techniques for determining the ].<ref>{{Cite news |title=Graphene Gazing Gives Glimpse Of Foundations Of Universe |url=http://www.sciencedaily.com/releases/2008/04/080403140918.htm |publisher=ScienceDaily |date=4 April 2008 }}</ref> | ||
| Graphene's ] can be tuned from 0 to 0.25 eV (about 5 micrometre wavelength) by applying voltage to a dual-gate bilayer graphene ] (FET) at room temperature.<ref>{{Cite journal | |
Graphene's ] can be tuned from 0 to 0.25 eV (about 5 micrometre wavelength) by applying voltage to a dual-gate bilayer graphene ] (FET) at room temperature.<ref>{{Cite journal |doi=10.1038/nature08105 |journal=Nature |last=Zhang |first=Y. |volume=459 |pages=820–823 |date=11 June 2009 |title=Direct observation of a widely tunable bandgap in bilayer graphene |pmid=19516337 |issue=7248 |bibcode=2009Natur.459..820Z |last2=Tang |first2=Tsung-Ta |last3=Girit |first3=Caglar |last4=Hao |first4=Zhao |last5=Martin |first5=Michael C. |last6=Zettl |first6=Alex |last7=Crommie |first7=Michael F. |last8=Shen |first8=Y. Ron |last9=Wang |first9=Feng |display-authors=9 }}</ref> The optical response of ] is tunable into the ] regime by an applied magnetic field.<ref>{{Cite journal |doi=10.1063/1.2964093 |journal=Appl Phys Lett |first=Junfeng |last=Liu |first2=A. R. |last2=Wright |first3=Chao |last3=Zhang |first4=Zhongshui |last4=Ma |volume=93 |pages=041106–041110 |date=29 July 2008 |title=Strong terahertz conductance of graphene nanoribbons under a magnetic field |bibcode=2008ApPhL..93d1106L |issue=4 }}</ref> Graphene/graphene oxide systems exhibit ], allowing tuning of both linear and ultrafast optical properties.<ref name="Kurum2011">{{Cite journal |last=Kurum |first=U. |title=Electrochemically tunable ultrafast optical response of graphene oxide |journal=Applied Physics Letters |volume=98 |page=141103 |year=2011 |bibcode=2011ApPhL..98b1103M |doi=10.1063/1.3540647 |issue=2 |last2=Liu |first2=Bo |last3=Zhang |first3=Kailiang |last4=Liu |first4=Yan |last5=Zhang |first5=Hao }}</ref> | ||
| A graphene-based ] (one-dimensional ]) has been fabricated and demonstrated its capability for excitation of surface electromagnetic waves in the periodic structure by using 633 nm He-Ne laser as the light source.<ref>{{cite journal | |
A graphene-based ] (one-dimensional ]) has been fabricated and demonstrated its capability for excitation of surface electromagnetic waves in the periodic structure by using 633 nm He-Ne laser as the light source.<ref>{{cite journal |first=K.V. |last=Sreekanth |title=Excitation of surface electromagnetic waves in a graphene-based Bragg grating |journal=Scientific Reports |year=2012 |doi=10.1038/srep00737 |pmid=23071901 |last2=Zeng |first2=Shuwen |last3=Shang |first3=Jingzhi |last4=Yong |first4=Ken-Tye |last5=Yu |first5=Ting |volume=2 |pages=737 |bibcode=2012NatSR...2E.737S |pmc=3471096 }}</ref> | ||
| ==== Saturable absorption ==== | ==== Saturable absorption ==== | ||
| Such unique absorption could become saturated when the input optical intensity is above a threshold value. This nonlinear optical behavior is termed ] and the threshold value is called the saturation fluence. Graphene can be saturated readily under strong excitation over the visible to ] region, due to the universal optical absorption and zero band gap. This has relevance for the mode locking of ]s, where fullband mode locking has been achieved by graphene-based saturable absorber. Due to this special property, graphene has wide application in ultrafast ]. Moreover, the optical response of graphene/graphene oxide layers can be tuned electrically.<ref name="Kurum2011" /><ref>{{cite journal | |
Such unique absorption could become saturated when the input optical intensity is above a threshold value. This nonlinear optical behavior is termed ] and the threshold value is called the saturation fluence. Graphene can be saturated readily under strong excitation over the visible to ] region, due to the universal optical absorption and zero band gap. This has relevance for the mode locking of ]s, where fullband mode locking has been achieved by graphene-based saturable absorber. Due to this special property, graphene has wide application in ultrafast ]. Moreover, the optical response of graphene/graphene oxide layers can be tuned electrically.<ref name="Kurum2011" /><ref>{{cite journal |last=Bao |first=Qiaoliang |title=Atomic-Layer Graphene as a Saturable Absorber for Ultrafast Pulsed Lasers |url=http://www3.ntu.edu.sg/home2006/zhan0174/AFM.pdf |format=PDF |archiveurl=http://web.archive.org/web/20110717122454/http://www3.ntu.edu.sg/home2006/zhan0174/AFM.pdf |archivedate=2011-07-17 |journal=Advanced Functional Materials |volume=19 |page=3077 |year=2009 |doi=10.1002/adfm.200901007 |issue=19 |last2=Zhang |first2=Han |last3=Wang |first3=Yu |last4=Ni |first4=Zhenhua |last5=Yan |first5=Yongli |last6=Shen |first6=Ze Xiang |last7=Loh |first7=Kian Ping |last8=Tang |first8=Ding Yuan }}<br/>{{Cite journal |last=Zhang |first=H. |title=Large energy mode locking of an erbium-doped fiber laser with atomic layer graphene |journal=Optics Express |volume=17 |page=P17630 |url=http://www3.ntu.edu.sg/home2006/zhan0174/OE_graphene.pdf |format=PDF |archiveurl=http://web.archive.org/web/20110717122606/http://www3.ntu.edu.sg/home2006/zhan0174/OE_graphene.pdf |archivedate=2011-07-17 |bibcode=2009OExpr..1717630Z |last2=Tang |first2=D. Y. |last3=Zhao |first3=L. M. |last4=Bao |first4=Q. L. |last5=Loh |first5=K. P. |year=2009 |doi=10.1364/OE.17.017630 |issue=20 |arxiv=0909.5536 }}<br/>{{Cite journal |last=Zhang |first=H. |last2=Bao |first2=Qiaoliang |last3=Tang |first3=Dingyuan |last4=Zhao |first4=Luming |last5=Loh |first5=Kianping |title=Large energy soliton erbium-doped fiber laser with a graphene-polymer composite mode locker |journal=Applied Physics Letters |volume=95 |page=P141103 |url=http://www3.ntu.edu.sg/home2006/zhan0174/apl.pdf |format=PDF |archiveurl=http://web.archive.org/web/20110717122745/http://www3.ntu.edu.sg/home2006/zhan0174/apl.pdf |format=PDF |archivedate=2011-07-17 |bibcode=2009ApPhL..95n1103Z |year=2009 |doi=10.1063/1.3244206 |issue=14 |arxiv=0909.5540 }}<br/> | ||
| {{Cite journal | |
{{Cite journal |last=Zhang |first=H. |last2=Tang |first2=Dingyuan |last3=Knize |first3=R. J. |last4=Zhao |first4=Luming |last5=Bao |first5=Qiaoliang |last6=Loh |first6=Kian Ping |title=Graphene mode locked, wavelength-tunable, dissipative soliton fiber laser |journal=Applied Physics Letters |volume=96 |page=111112 |url=http://www.sciencenet.cn/upload/blog/file/2010/3/20103191224576536.pdf |format=PDF |archiveurl=http://www.webcitation.org/5pt6I3oAm |archivedate=2010-05-21 |doi=10.1063/1.3367743 |bibcode=2010ApPhL..96k1112Z |year=2010 |issue=11|arxiv=1003.0154 }}, {{cite journal |last=Zhang |title=Graphene: Mode-locked lasers |journal=NPG Asia Materials |year=2009 |doi=10.1038/asiamat.2009.52 }}</ref> | ||
| Saturable absorption in graphene could occur at the Microwave and Terahertz band, owing to its wideband optical absorption property. The microwave saturable absorption in graphene demonstrates the possibility of graphene microwave and terahertz photonics devices, such as microwave saturable absorber, modulator, polarizer, microwave signal processing and broad-band wireless access networks.<ref name=Zheng>{{Cite journal | |
Saturable absorption in graphene could occur at the Microwave and Terahertz band, owing to its wideband optical absorption property. The microwave saturable absorption in graphene demonstrates the possibility of graphene microwave and terahertz photonics devices, such as microwave saturable absorber, modulator, polarizer, microwave signal processing and broad-band wireless access networks.<ref name=Zheng>{{Cite journal |last=Zheng |first=Z. |last2=Zhao |first2=Chujun |last3=Lu |first3=Shunbin |last4=Chen |first4=Yu |last5=Li |first5=Ying |last6=Zhang |first6=Han |last7=Wen |first7=Shuangchun|title=Microwave and optical saturable absorption in graphene |journal=Optics Express |year=2012 |volume=20 |issue=21 |pages=23201–23214 |doi=10.1364/OE.20.023201 |url=http://www.opticsinfobase.org/view_article.cfm?gotourl=http%3A%2F%2Fwww.opticsinfobase.org%2FDirectPDFAccess%2FDDD3E2E7-B65E-B0FE-CE508B2B58C39140_242486%2Foe-20-21-23201.pdf%3Fda%3D1%26id%3D242486%26seq%3D0%26mobile%3Dno&org= |format=PDF |pmid=23188285 |bibcode=2012OExpr..2023201Z }}</ref> | ||
| ==== Nonlinear Kerr effect ==== | ==== Nonlinear Kerr effect ==== | ||
| Under more intensive laser illumination, graphene could also possess a nonlinear phase shift due to the optical nonlinear ]. Based on a typical open and close aperture z-scan measurement, graphene possesses a giant non-linear Kerr coefficient of {{val|e=-7|u=cm<sup>2</sup>·W<sup>−1</sup>}}, almost nine orders of magnitude larger than that of bulk dielectrics.<ref name=ZHANGHAN>{{ Cite journal | |
Under more intensive laser illumination, graphene could also possess a nonlinear phase shift due to the optical nonlinear ]. Based on a typical open and close aperture z-scan measurement, graphene possesses a giant non-linear Kerr coefficient of {{val|e=-7|u=cm<sup>2</sup>·W<sup>−1</sup>}}, almost nine orders of magnitude larger than that of bulk dielectrics.<ref name="ZHANGHAN">{{ Cite journal |last=Zhang |first=H. |title=Z-scan measurement of the nonlinear refractive index of graphene |journal=Optics Letters |year=2012 |volume=37 |issue=11 |pages=1856–1858 |doi=10.1364/OL.37.001856 |pmid=22660052 |last2=Virally |first2=Stéphane |last3=Bao |first3=Qiaoliang |last4=Kian Ping |first4=Loh |last5=Massar |first5=Serge |last6=Godbout |first6=Nicolas |last7=Kockaert |first7=Pascal |bibcode=2012OptL...37.1856Z }}</ref> This suggests that graphene may be a nonlinear Kerr medium, paving the way for graphene-based nonlinear Kerr photonics such as a ]. | ||
| === Excitonic === | === Excitonic === | ||
| First-principle calculations with quasiparticle corrections and many-body effects are performed to study the electronic and optical properties of graphene-based materials. The approach is described as three stages.<ref>{{cite journal |journal=Rev. Mod. Phys. |year=2002 |volume=74 |page=601 |doi=10.1103/RevModPhys.74.601 |bibcode=2002RvMP...74..601O |title=Electronic excitations: Density-functional versus many-body Green's-function approaches | |
First-principle calculations with quasiparticle corrections and many-body effects are performed to study the electronic and optical properties of graphene-based materials. The approach is described as three stages.<ref>{{cite journal |journal=Rev. Mod. Phys. |year=2002 |volume=74 |page=601 |doi=10.1103/RevModPhys.74.601 |bibcode=2002RvMP...74..601O |title=Electronic excitations: Density-functional versus many-body Green's-function approaches |last=Onida |first=Giovanni |last2=Rubio |first2=Angel |last3=Rubio |first3=Angel |issue=2 }}</ref> With GW calculation, the properties of graphene-based materials are accurately investigated, including graphene,<ref>{{cite journal |journal=Physical Review Letters |year=2009 |volume=103 |page=186802 |doi=10.1103/PhysRevLett.103.186802 |bibcode=2009PhRvL.103r6802Y |title=Excitonic Effects on the Optical Response of Graphene and Bilayer Graphene |last=Yang |first=Li |last2=Deslippe |first2=Jack |last3=Park |first3=Cheol-Hwan |last4=Cohen |first4=Marvin |last5=Louie |first5=Steven |issue=18 |pmid=19905823|arxiv=0906.0969 }}</ref> ],<ref>{{cite journal |journal=Physical Review B |year=2008 |volume=77 |page=041404 |doi=10.1103/PhysRevB.77.041404 |title=Optical properties of graphene nanoribbons: The role of many-body effects |last=Prezzi |first=Deborah |last2=Varsano |first2=Daniele |last3=Ruini |first3=Alice |last4=Marini |first4=Andrea |last5=Molinari |first5=Elisa |issue=4|arxiv=0706.0916 |bibcode=2008PhRvB..77d1404P }}<br/>{{cite journal |journal=Nano Lett. |year=2007 |volume=7 |pages=3112–5 |doi=10.1021/nl0716404 |title=Excitonic Effects in the Optical Spectra of Graphene Nanoribbons |last=Yang |first=Li |last2=Cohen |first2=Marvin L. |last3=Louie |first3=Steven G. |issue=10 |pmid=17824720|arxiv=0707.2983 |bibcode=2007NanoL...7.3112Y }}<br/>{{cite journal |journal=Physical Review Letters |year=2008 |volume=101 |page=186401 |doi=10.1103/PhysRevLett.101.186401 |bibcode=2008PhRvL.101r6401Y |title=Magnetic Edge-State Excitons in Zigzag Graphene Nanoribbons |last=Yang |first=Li |last2=Cohen |first2=Marvin L. |last3=Louie |first3=Steven G. |issue=18 |pmid=18999843 }}</ref> edge and surface functionalized armchair graphene nanoribbons,<ref>{{cite journal |journal=J. Phys. Chem. C |year=2010 |volume=114 |page=17257 |doi=10.1021/jp102341b |title=Excitons of Edge and Surface Functionalized Graphene Nanoribbons |last=Zhu |first=Xi |last2=Su |first2=Haibin |issue=41 }}</ref> hydrogen saturated armchair graphene nanoribbons,<ref>{{cite journal |journal=Nanoscale |year=2011 |volume=3 |pages=2324–8 |doi=10.1039/c1nr10095e |title=Excitonic properties of hydrogen saturation-edged armchair graphene nanoribbons |last=Wang |first=Min |last2=Li |first2=Chang Ming |issue=5 |pmid=21503364 |bibcode=2011Nanos...3.2324W }}</ref> ] in graphene SNS junctions with single localized defect<ref>{{Cite journal ||first=Dima |last=Bolmatov |first2=Chung-Yu |last2=Mou |title=Josephson effect in graphene SNS junction with a single localized defect |journal=Physica B |volume=405 |page=2896 |year=2010 |doi=10.1016/j.physb.2010.04.015 |issue=13|arxiv=1006.1391 |bibcode=2010PhyB..405.2896B }}<br/>{{Cite journal |first=Dima |last=Bolmatov |first2=Chung-Yu |last2=Mou |title=Tunneling conductance of the graphene SNS junction with a single localized defect |journal=Journal of Experimental and Theoretical Physics (JETP) |volume=110 |page=613 |year=2010 |doi=10.1134/S1063776110040084 |issue=4|arxiv=1006.1386 |bibcode=2010JETP..110..613B }}</ref> and scaling properties in armchair graphene nanoribbons.<ref>{{cite journal |title=Scaling of Excitons in Graphene Nanoribbons with Armchair Shaped Edges |journal=Journal of Physical Chemistry A |year=2011 |volume=115 |issue=43 |pages=11998–12003 |doi=10.1021/jp202787h |last=Zhu |first=Xi |last2=Su |first2=Haibin }}</ref> | ||
| === Thermal === | === Thermal === | ||
| Line 195: | Line 176: | ||
| ==== Stability ==== | ==== Stability ==== | ||
| ] show that a graphene sheet is thermodynamically unstable if its size is less than about 20 nm (“graphene is the least stable structure until about 6000 atoms”) and becomes the most stable ] (as within graphite) only for molecules larger than 24,000 atoms.<ref name=stability>{{Cite journal | |
] show that a graphene sheet is thermodynamically unstable if its size is less than about 20 nm (“graphene is the least stable structure until about 6000 atoms”) and becomes the most stable ] (as within graphite) only for molecules larger than 24,000 atoms.<ref name=stability>{{Cite journal |first=O. B. |last=Shenderova |first2=V. V. |last2=Zhirnov |first3=D. W. |last3=Brenner |year=2002 |title=Carbon Nanostructures |journal=Critical Reviews in Solid State and Materials Sciences |volume=27 |page=227 |doi=10.1080/10408430208500497 |bibcode=2002CRSSM..27..227S |issue=3–4 }}</ref> | ||
| ==== Conductivity ==== | ==== Conductivity ==== | ||
| The near-room temperature ] of graphene was measured to be between (4.84±0.44) × 10<sup>3</sup> to (5.30±0.48) × 10<sup>3</sup> W·m<sup>−1</sup>·K<sup>−1</sup>. These measurements, made by a non-contact optical technique, are in excess of those measured for carbon nanotubes or diamonds. The isotopic composition, the ratio of ] to ], has a significant impact on thermal conductivity, where isotopically pure <sup>12</sup>C graphene has higher conductivity than either a 50:50 isotope ratio or the naturally occurring 99:1 ratio.<ref name=chen2012natmat>{{Cite journal |first=Shanshan | The near-room temperature ] of graphene was measured to be between (4.84±0.44) × 10<sup>3</sup> to (5.30±0.48) × 10<sup>3</sup> W·m<sup>−1</sup>·K<sup>−1</sup>. These measurements, made by a non-contact optical technique, are in excess of those measured for carbon nanotubes or diamonds. The isotopic composition, the ratio of ] to ], has a significant impact on thermal conductivity, where isotopically pure <sup>12</sup>C graphene has higher conductivity than either a 50:50 isotope ratio or the naturally occurring 99:1 ratio.<ref name=chen2012natmat>{{Cite journal |first=Shanshan | ||
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|last=Chen |first2=Qingzhi |last2=Wu |first3=Columbia |last3=Mishra |first4=Junyong |last4=Kang |first5=Hengji |last5=Zhang | ||
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|first6=Kyeongjae |last6=Cho |first7=Weiwei |last7=Cai |first8=Alexander A. |last8=Balandin |first9=Rodney S. |last9=Ruoff | ||
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|publication-date=2012-01-10 |title=Thermal conductivity of isotopically modified graphene |journal=] | ||
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|volume=11 |issue=3 |page=203 |pmid= |doi=10.1038/nmat3207 |year=2012 |arxiv=1112.5752 |bibcode=2012NatMa..11..203C |display-authors=9 }}<br />''Lay summary'': {{Cite news |publication-date=2012-01-12 |title=Keeping Electronics Cool | ||
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|periodical=] |at=scientificcomputing.com | ||
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|publisher=] | ||
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|url=http://www.scientificcomputing.com/news-HPC-Keeping-Electronics-Cool-011212.aspx?et_cid=2422972&et_rid=220285420&linkid=http%3a%2f%2fwww.scientificcomputing.com%2fnews-HPC-Keeping-Electronics-Cool-011212.aspx |first=Suzanne |last=Tracy |date=12 January 2012 }}</ref> It can be shown by using the ], that the thermal conduction is ]-dominated.<ref name="Balandin">{{Cite journal |last=Balandin |first=A. A. |date=20 February 2008 | ||
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|doi=10.1021/nl0731872 |title=Superior Thermal Conductivity of Single-Layer Graphene |journal=] | ||
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|pmid=18284217 |volume=8 |issue=3 |pages=902–907 |bibcode=2008NanoL...8..902B |last2=Ghosh |first2=Suchismita |last3=Bao |first3=Wenzhong |last4=Calizo |first4=Irene |last5=Teweldebrhan |first5=Desalegne |last6=Miao |first6=Feng |last7=Lau |first7=Chun Ning | ||
| }}</ref> However, for a gated graphene strip, an applied gate bias causing a ] shift much larger than k<sub>B</sub>T can cause the electronic contribution to increase and dominate over the ] contribution at low temperatures. The ballistic thermal conductance of graphene is isotropic.<ref name="Saito">{{Cite journal |journal=] | |||
| |first3=Wenzhong |last4=Calizo | |||
| |last=Saito |first=K. |last2=Nakamura |first2=J. |last3=Natori |first3=A. |title=Ballistic thermal conductance of a graphene sheet | |||
| |first4=Irene |last5=Teweldebrhan | |||
| |volume=76 |page=115409 |year=2007 |doi=10.1103/PhysRevB.76.115409 |bibcode=2007PhRvB..76k5409S |issue=11 | |||
| |first5=Desalegne |last6=Miao | |||
| }}</ref><ref name="Qizhen Liang, Xuxia Yao, Wei Wang, Yan Liu, Ching Ping Wong. 2011 2392–2401">{{cite journal |first=Qizhen |last=Liang |first2=Xuxia |last2=Yao |first3=Wei |last3=Wang |first4=Yan |last4=Liu |first5=Ching Ping |last5=Wong |year=2011 |title=A Three-Dimensional Vertically Aligned Functionalized Multilayer Graphene Architecture: An Approach for Graphene-Based Thermal Interfacial Materials |journal=ACS Nano |pmid=21384860 |volume=5 |issue=3 |pages=2392–2401 |doi=10.1021/nn200181e }}</ref> | |||
| |first6=Feng |last7=Lau | |||
| |first7=Chun Ning | |||
| |last2=Ghosh | |||
| }}</ref> However, for a gated graphene strip, an applied gate bias causing a ] shift much larger than k<sub>B</sub>T can cause the electronic contribution to increase and dominate over the ] contribution at low temperatures. The ballistic thermal conductance of graphene is isotropic.<ref name="Saito">{{Cite journal |journal=] | |||
| | author=Saito, K., Nakamura, J., and Natori, A. |title=Ballistic thermal conductance of a graphene sheet | |||
| | volume=76 |page=115409 |year=2007 |doi=10.1103/PhysRevB.76.115409 |bibcode=2007PhRvB..76k5409S |issue=11 | |||
| }}</ref><ref name="Qizhen Liang, Xuxia Yao, Wei Wang, Yan Liu, Ching Ping Wong. 2011 2392–2401">{{cite journal |author= Qizhen Liang, Xuxia Yao, Wei Wang, Yan Liu, Ching Ping Wong. |year= 2011 |title= A Three-Dimensional Vertically Aligned Functionalized Multilayer Graphene Architecture: An Approach for Graphene-Based Thermal Interfacial Materials |journal= ACS Nano |pmid= 21384860 |volume=5 |issue= 3 |pages= 2392–2401 |doi= 10.1021/nn200181e}}</ref> | |||
| Potential for this high conductivity can be seen by considering graphite, a 3D version of graphene that has ] ] of over a {{val|1000|u=W·m<sup>−1</sup>·K<sup>−1</sup>}} (comparable to ]). In graphite, the c-axis (out of plane) thermal conductivity is over a factor of ~100 smaller due to the weak binding forces between basal planes as well as the larger ].<ref>{{Cite book |url=http://books.google.com/?id=7p2pgNOWPbEC |title=Graphite and Precursors | |
Potential for this high conductivity can be seen by considering graphite, a 3D version of graphene that has ] ] of over a {{val|1000|u=W·m<sup>−1</sup>·K<sup>−1</sup>}} (comparable to ]). In graphite, the c-axis (out of plane) thermal conductivity is over a factor of ~100 smaller due to the weak binding forces between basal planes as well as the larger ].<ref>{{Cite book |url=http://books.google.com/?id=7p2pgNOWPbEC |title=Graphite and Precursors |last=Delhaes |first=P. |publisher=CRC Press |year=2001 |isbn=90-5699-228-7 }}</ref> In addition, the ballistic thermal conductance of graphene is shown to give the lower limit of the ballistic thermal conductances, per unit circumference, length of carbon nanotubes.<ref name="mingo">{{Cite journal |last=Mingo |first=N. |last2=Broido |first2=D.A. |title=Carbon Nanotube Ballistic Thermal Conductance and Its Limits |doi=10.1103/PhysRevLett.95.096105 |journal=Physical Review Letters |volume=95 |page=096105 |year=2005 |bibcode=2005PhRvL..95i6105M |issue=9 }}</ref> | ||
| Despite its 2-D nature, graphene has 3 ] modes. The two in-plane modes (LA, TA) have a linear ], whereas the out of plane mode (ZA) has a quadratic dispersion relation. Due to this, the T<sup>2</sup> dependent thermal conductivity contribution of the linear modes is dominated at low temperatures by the T<sup>1.5</sup> contribution of the out of plane mode.<ref name="mingo"/> Some graphene phonon bands display negative ]s.<ref name="mounet">{{Cite journal | |
Despite its 2-D nature, graphene has 3 ] modes. The two in-plane modes (LA, TA) have a linear ], whereas the out of plane mode (ZA) has a quadratic dispersion relation. Due to this, the T<sup>2</sup> dependent thermal conductivity contribution of the linear modes is dominated at low temperatures by the T<sup>1.5</sup> contribution of the out of plane mode.<ref name="mingo"/> Some graphene phonon bands display negative ]s.<ref name="mounet">{{Cite journal |last=Mounet |first=N. |last2=Marzari |first2=N. |title=First-principles determination of the structural, vibrational and thermodynamic properties of diamond, graphite, and derivatives |doi=10.1103/PhysRevB.71.205214 |journal=Physical Review B |volume=71 |page=205214 |year=2005 |arxiv=cond-mat/0412643 |bibcode=2005PhRvB..71t5214M |issue=20 }}</ref> At low temperatures (where most optical modes with positive Grüneisen parameters are still not excited) the contribution from the negative Grüneisen parameters will be dominant and ] (which is directly proportional to Grüneisen parameters) negative. The lowest negative Grüneisen parameters correspond to the lowest transversal acoustic ZA modes. Phonon frequencies for such modes increase with the in-plane ] since atoms in the layer upon stretching will be less free to move in the z direction. This is similar to the behavior of a string, which, when it is stretched, will have vibrations of smaller amplitude and higher frequency. This phenomenon, named "membrane effect", was predicted by ] in 1952.<ref name="lifshitz">{{Cite journal |last=Lifshitz |first=I.M. |journal=Journal of Experimental and Theoretical Physics (in Russian) |volume=22 |page=475 |year=1952 }}</ref> | ||
| === Mechanical === | === Mechanical === | ||
| The flat graphene sheet is unstable with respect to scrolling i.e. bending into a cylindrical shape, which is its lower-energy state.<ref name=nmscrolling>{{Cite journal | |
The flat graphene sheet is unstable with respect to scrolling i.e. bending into a cylindrical shape, which is its lower-energy state.<ref name="nmscrolling">{{Cite journal |first=S. |last=Braga |first2=V. R. |last2=Coluci |first3=S. B. |last3=Legoas |first4=R. |last4=Giro |first5=D. S. |last5=Galvão |first6=R. H. |last6=Baughman |year=2004 |title=Structure and Dynamics of Carbon Nanoscrolls |journal=Nano Letters |volume=4 |page=881 |doi=10.1021/nl0497272 |bibcode=2004NanoL...4..881B |issue=5 }}</ref> | ||
| As of 2009, graphene appeared to be one of the strongest materials known with a ] over 100 times greater than a hypothetical ] film of the same (thin) thickness,<ref name="nobelprize.org">. nobelprize.org.</ref> with a ] | As of 2009, graphene appeared to be one of the strongest materials known with a ] over 100 times greater than a hypothetical ] film of the same (thin) thickness,<ref name="nobelprize.org">. nobelprize.org.</ref> with a ] | ||
| (stiffness) of {{val|1|u=TPa}} ({{val|fmt=commas|150000000|u=]}}).<ref name=lee>{{Cite journal | |
(stiffness) of {{val|1|u=TPa}} ({{val|fmt=commas|150000000|u=]}}).<ref name=lee>{{Cite journal |last=Lee |first=C. |title=Measurement of the Elastic Properties and Intrinsic Strength of Monolayer Graphene |journal=Science |volume=321 |year=2008 |laysummary=http://web.archive.org/web/20110629131809/http://www.aip.org/isns/reports/2008/027.html |doi=10.1126/science.1157996 |pmid=18635798 |issue=5887 |bibcode=2008Sci...321..385L |pages=385–8 |last2=Wei |first2=X. |last3=Kysar |first3=J. W. |last4=Hone |first4=J. }}</ref> The Nobel announcement illustrated this by saying that a 1 square meter graphene hammock would support a {{val|4|u=kg}} cat but would weigh only as much as one of the cat's whiskers, at 0.77 mg (about 0.001% of the weight of 1 m<sup>2</sup> of paper).<ref name="nobelprize.org"/> | ||
| However, the process of separating it from graphite, where it occurs naturally, requires technological development to be economical enough to be used in industrial processes.<ref name="nypost">{{cite news |url |
However, the process of separating it from graphite, where it occurs naturally, requires technological development to be economical enough to be used in industrial processes.<ref name="nypost">{{cite news |url=http://www.nypost.com/seven/08252008/news/regionalnews/toughest_stuff__known_to_man_125993.htm |title=Toughest Stuff Known to Man: Discovery Opens Door to Space Elevator |first=Bill |last=Sanderson |publisher=nypost.com |date=25 August 2008 }}</ref><ref name="ScienceDaily">{{cite web |url=http://www.sciencedaily.com/releases/2010/01/100119111057.htm |title=Breakthrough in Developing Super-Material Graphene |publisher=ScienceDaily |date=20 January 2010 }}</ref> | ||
| The ] of suspended graphene sheets has been measured using an ] (AFM). Graphene sheets, held together by van der Waals forces, were suspended over {{chem|SiO|2}} cavities where an AFM tip was probed to test its mechanical properties. Its spring constant was in the range 1–5 N/m and the stiffness was {{val|0.5|u=TPa}}, which differs from that of bulk graphite. These high values make graphene very strong and rigid. These intrinsic properties could lead to using graphene for ] applications such as pressure sensors and resonators.<ref>{{Cite journal | |
The ] of suspended graphene sheets has been measured using an ] (AFM). Graphene sheets, held together by van der Waals forces, were suspended over {{chem|SiO|2}} cavities where an AFM tip was probed to test its mechanical properties. Its spring constant was in the range 1–5 N/m and the stiffness was {{val|0.5|u=TPa}}, which differs from that of bulk graphite. These high values make graphene very strong and rigid. These intrinsic properties could lead to using graphene for ] applications such as pressure sensors and resonators.<ref>{{Cite journal |last=Frank |first=I. W. |last2=Tanenbaum |first2=D. M. |last3=Van Der Zande |first3=A.M. |last4=McEuen |first4=P. L. |title=Mechanical properties of suspended graphene sheets |doi=10.1116/1.2789446 |journal=J. Vac. Sci. Technol. B |volume=25 |pages=2558–2561 |year=2007 |url=http://www.lassp.cornell.edu/lassp_data/mceuen/homepage/Publications/JVSTB_Pushing_Graphene.pdf |format=PDF |bibcode=2007JVSTB..25.2558F |issue=6 }}</ref> | ||
| As is true of all materials, regions of graphene are subject to thermal and quantum fluctuations in relative displacement. Although the amplitude of these fluctuations is bounded in 3D structures (even in the limit of infinite size), the ] shows that the amplitude of long-wavelength fluctuations grows logarithmically with the scale of a 2D structure, and would therefore be unbounded in structures of infinite size. Local deformation and elastic strain are negligibly affected by this long-range divergence in relative displacement. It is believed that a sufficiently large 2D structure, in the absence of applied lateral tension, will bend and crumple to form a fluctuating 3D structure. Researchers have observed ripples in suspended layers of graphene,<ref name=Meyer07/> and it has been proposed that the ripples are caused by thermal fluctuations in the material. As a consequence of these dynamical deformations, it is debatable whether graphene is truly a 2D structure.{{sfn|Geim|Novoselov|2007}}<ref name="Carlsson"/><ref name="Fasolino"/><ref>{{Cite journal | |
As is true of all materials, regions of graphene are subject to thermal and quantum fluctuations in relative displacement. Although the amplitude of these fluctuations is bounded in 3D structures (even in the limit of infinite size), the ] shows that the amplitude of long-wavelength fluctuations grows logarithmically with the scale of a 2D structure, and would therefore be unbounded in structures of infinite size. Local deformation and elastic strain are negligibly affected by this long-range divergence in relative displacement. It is believed that a sufficiently large 2D structure, in the absence of applied lateral tension, will bend and crumple to form a fluctuating 3D structure. Researchers have observed ripples in suspended layers of graphene,<ref name=Meyer07/> and it has been proposed that the ripples are caused by thermal fluctuations in the material. As a consequence of these dynamical deformations, it is debatable whether graphene is truly a 2D structure.{{sfn|Geim|Novoselov|2007}}<ref name="Carlsson"/><ref name="Fasolino"/><ref>{{Cite journal |first=Dima |last=Bolmatov |first2=Chung-Yu |last2=Mou |title=Graphene-based modulation-doped superlattice structures |journal=Journal of Experimental and Theoretical Physics (JETP) |volume=112 |page=102 |year=2011 |doi=10.1134/S1063776111010043|arxiv=1011.2850 |bibcode=2011JETP..112..102B }}<br/>{{Cite journal |first=Dima |last=Bolmatov |title=Thermodynamic properties of tunneling quasiparticles in graphene-based structures |journal=Physica C |volume=471 |page=1651 |year=2011 |doi=10.1016/j.physc.2011.07.008 |issue=23–24|arxiv=1106.6331 |bibcode=2011PhyC..471.1651B }}</ref> | ||
| === Spin transport === | === Spin transport === | ||
| Graphene is claimed to be an ideal material for ] due to its small ] and the near absence of ]s in carbon (as well as a weak ]). Electrical ] injection and detection has been demonstrated up to room temperature.<ref name="Tombros">{{cite journal | |
Graphene is claimed to be an ideal material for ] due to its small ] and the near absence of ]s in carbon (as well as a weak ]). Electrical ] injection and detection has been demonstrated up to room temperature.<ref name="Tombros">{{cite journal |title=Electronic spin transport and spin precession in single graphene layers at room temperature |bibcode=2007Natur.448..571T |last=Tombros |first=Nikolaos |author2=et al. |journal=Nature |year=2007 |format=PDF |volume=448 |issue=7153 |pages=571–575 |doi=10.1038/nature06037 |pmid=17632544 |arxiv=0706.1948 }}</ref><ref name="ChoSpin"> | ||
| {{Cite journal | |
{{Cite journal |first=Sungjae |last=Cho |first2=Yung-Fu |last2=Chen |first3=Michael S. |last3=Fuhrer |year=2007 |volume=91 |page=123105 |title=Gate-tunable Graphene Spin Valve |journal=Applied Physics Letters |doi=10.1063/1.2784934 | ||
| | |
|bibcode=2007ApPhL..91l3105C |issue=12 |arxiv=0706.1597 }}</ref><ref name="Ohishi">{{Cite journal |last=Ohishi |first=Megumi |author2=et al. |year=2007 |volume=46 |pages=L605–L607 |title=Spin Injection into a Graphene Thin Film at Room Temperature |journal=Jpn J Appl Phys |doi=10.1143/JJAP.46.L605 |bibcode=2007JaJAP..46L.605O |arxiv=0706.1451 }}</ref> Spin coherence length above 1 micrometre at room temperature was observed,<ref name="Tombros"/> and control of the spin current polarity with an electrical gate was observed at low temperature.<ref name="ChoSpin"/> | ||
| === Anomalous quantum Hall effect === | === Anomalous quantum Hall effect === | ||
| Line 248: | Line 223: | ||
| The ] is relevant for accurate measuring of electrical quantities, and in 1985 ] received the ] for its discovery. The effect concerns the dependence of a transverse conductivity on a ], which is perpendicular to a current-carrying stripe. Usually the phenomenon, the quantization of the so-called ] <math>\sigma_{xy}</math> at integer multiples (the "]") of the basic quantity <math>e^2/h</math> (where ''e'' is the elementary electric charge and ''h'' is ]) can be observed only in very clean ] or ] solids at very low temperatures around 3 ] and very high magnetic fields. | The ] is relevant for accurate measuring of electrical quantities, and in 1985 ] received the ] for its discovery. The effect concerns the dependence of a transverse conductivity on a ], which is perpendicular to a current-carrying stripe. Usually the phenomenon, the quantization of the so-called ] <math>\sigma_{xy}</math> at integer multiples (the "]") of the basic quantity <math>e^2/h</math> (where ''e'' is the elementary electric charge and ''h'' is ]) can be observed only in very clean ] or ] solids at very low temperatures around 3 ] and very high magnetic fields. | ||
| In contrast graphene shows the quantum Hall effect just in the presence of a magnetic field and just with respect to conductivity-quantization: the effect is ''anomalous'' in that the sequence of steps is shifted by 1/2 with respect to the standard sequence and with an additional factor of 4. Graphene's Hall conductivity is <math>\sigma_{xy} |
In contrast graphene shows the quantum Hall effect just in the presence of a magnetic field and just with respect to conductivity-quantization: the effect is ''anomalous'' in that the sequence of steps is shifted by 1/2 with respect to the standard sequence and with an additional factor of 4. Graphene's Hall conductivity is <math>\sigma_{xy}=\pm {4\cdot\left(N + 1/2 \right)e^2}/h </math>, where ''N'' is the Landau level and the double valley and double spin degeneracies give the factor of 4.{{sfn|Geim|Novoselov|2007}} Moreover, in graphene these anomalies are present at room temperature, i.e. at roughly {{val|20|u=°C}}.<ref name="2dgasDiracFermions"/> This anomalous behavior is a direct result of graphene's massless Dirac electrons. In a magnetic field, their spectrum has a Landau level with energy precisely at the Dirac point. This level is a consequence of the ] and is half-filled in neutral graphene,<ref name="Semenoff"/> leading to the "+1/2" in the Hall conductivity.<ref name="Gusynin">{{Cite journal |last=Gusynin |first=V. P. |last2=Sharapov |first2=S. G. |title=Unconventional Integer Quantum Hall Effect in Graphene |doi=10.1103/PhysRevLett.95.146801 |journal=Physical Review Letters |volume=95 |page=146801 |year=2005 |pmid=16241680 |bibcode=2005PhRvL..95n6801G |arxiv=cond-mat/0506575 |issue=14 }}</ref> Bilayer graphene also shows the quantum Hall effect, but with only one of the two anomalies (i.e. <math>\sigma_{xy}=\pm {4\cdot N\cdot e^2}/h </math>). In the second anomaly, the first plateau at ''N=0'' is absent, indicating that bilayer graphene stays metallic at the neutrality point.{{sfn|Geim|Novoselov|2007}} | ||
| Unlike normal metals, graphene's longitudinal resistance shows maxima rather than minima for integral values of the Landau filling factor in measurements of the ], which show a phase shift of π, known as ].<ref name="2dgasDiracFermions"/><ref name="E-Phonon"/> Berry’s phase arises due to the zero effective carrier mass near the Dirac points.<ref name="Berry'sPhase">{{Cite journal | |
Unlike normal metals, graphene's longitudinal resistance shows maxima rather than minima for integral values of the Landau filling factor in measurements of the ], which show a phase shift of π, known as ].<ref name="2dgasDiracFermions"/><ref name="E-Phonon"/> Berry’s phase arises due to the zero effective carrier mass near the Dirac points.<ref name="Berry'sPhase">{{Cite journal |last=Zhang |first=Y. |last2=Tan |first2=Y. W. |last3=Stormer |first3=H. L. |last4=Kim |first4=P. |title=Experimental observation of the quantum Hall effect and Berry's phase in graphene |doi=10.1038/nature04235 |journal=Nature |volume=438 |pages=201–204 |year=2005 |pmid=16281031 |issue=7065 |arxiv=cond-mat/0509355 |bibcode=2005Natur.438..201Z }}</ref> Study of the temperature dependence of graphene's Shubnikov–de Haas oscillations reveals that the carriers have a non-zero cyclotron mass, despite their zero effective mass from the E–k relation.<ref name="2dgasDiracFermions"/> | ||
| Graphene samples prepared on nickel films, and on both the silicon face and carbon face of ], show the ] directly in electrical measurements.<ref name="ByungHeeHong"/><ref name="0908.1900"/><ref name="ShenAPL"/><ref name=0909.2903/><ref name=0909.1193/><ref name=phase1/> Graphitic layers on the carbon face of silicon carbide show a clear ] in ] experiments, and the anomalous quantum Hall effect is observed in cyclotron resonance and tunneling experiments.<ref name="Fuhrer09">{{Cite journal | |
Graphene samples prepared on nickel films, and on both the silicon face and carbon face of ], show the ] directly in electrical measurements.<ref name="ByungHeeHong"/><ref name="0908.1900"/><ref name="ShenAPL"/><ref name=0909.2903/><ref name=0909.1193/><ref name=phase1/> Graphitic layers on the carbon face of silicon carbide show a clear ] in ] experiments, and the anomalous quantum Hall effect is observed in cyclotron resonance and tunneling experiments.<ref name="Fuhrer09">{{Cite journal |first=Michael S. |last=Fuhrer |title=A physicist peels back the layers of excitement about graphene|doi=10.1038/4591037e |journal=Nature |volume=459 |page=1037 |year=2009 |pmid=19553953|issue=7250 |bibcode=2009Natur.459.1037F }}</ref> | ||
| ==== Strong magnetic fields ==== | ==== Strong magnetic fields ==== | ||
| Graphene's quantum Hall effect in magnetic fields above 10 ]s or so reveals additional interesting features. Additional plateaus of the Hall conductivity at <math>\sigma_{xy} |
Graphene's quantum Hall effect in magnetic fields above 10 ]s or so reveals additional interesting features. Additional plateaus of the Hall conductivity at <math>\sigma_{xy}=\nu e^2/h</math> with <math>\nu=0,\pm {1},\pm {4}</math> are observed.<ref name="nu-0-1-4">{{Cite journal |last=Zhang |first=Y. |title=Landau-Level Splitting in Graphene in High Magnetic Fields |doi=10.1103/PhysRevLett.96.136806 |journal=Physical Review Letters |volume=96 |page=136806 |year=2006 |bibcode=2006PhRvL..96m6806Z |issue=13 |last2=Jiang |first2=Z. |last3=Small |first3=J. P. |last4=Purewal |first4=M. S. |last5=Tan |first5=Y.-W. |last6=Fazlollahi |first6=M. |last7=Chudow |first7=J. D. |last8=Jaszczak |first8=J. A. |last9=Stormer |first9=H. L. |last10=Kim |first10=P. |arxiv=cond-mat/0602649 }}</ref> Also, the observation of a plateau at <math>\nu=3</math><ref name="nu-3">{{Cite journal |last=Du |first=X. |title=Fractional quantum Hall effect and insulating phase of Dirac electrons in graphene |doi=10.1038/nature08522 |journal=Nature |volume=462 |pages=192–195 |year=2009 |issue=7270 |pmid=19829294 |last2=Skachko |first2=Ivan |last3=Duerr |first3=Fabian |last4=Luican |first4=Adina |last5=Andrei |first5=Eva Y.|arxiv=0910.2532 |bibcode=2009Natur.462..192D }}</ref> and the fractional quantum Hall effect at <math>\nu=1/3</math> were reported.<ref name="nu-3"/><ref name="nu-one3rd">{{Cite journal |last=Bolotin |first=K. |last2=Ghahari |first2=Fereshte |last3=Shulman |first3=Michael D. |last4=Stormer |first4=Horst L. |last5=Kim |first5=Philip |title=Observation of the fractional quantum Hall effect in graphene |doi=10.1038/nature08582 |journal=Nature |volume=462 |pages=196–199 |year=2009 |issue=7270 |pmid=19881489 |arxiv=0910.2763 |bibcode=2009Natur.462..196B }}</ref> | ||
| These observations with <math>\nu |
These observations with <math>\nu=0,\pm 1,\pm 3, \pm 4</math> indicate that the four-fold degeneracy (two valley and two spin degrees of freedom) of the Landau energy levels is partially or completely lifted. One hypothesis is that the ] of ] is responsible for lifting the degeneracy.{{citation needed|date=December 2013}} | ||
| == Forms == | == Forms == | ||
| Line 264: | Line 239: | ||
| === Nanostripes === | === Nanostripes === | ||
| ] ("nanostripes" in the "zig-zag" orientation), at low temperatures, show spin-polarized metallic edge currents, which also suggests applications in the new field of ]. (In the "armchair" orientation, the edges behave like semiconductors.<ref name="Castro">{{Cite journal | |
] ("nanostripes" in the "zig-zag" orientation), at low temperatures, show spin-polarized metallic edge currents, which also suggests applications in the new field of ]. (In the "armchair" orientation, the edges behave like semiconductors.<ref name="Castro">{{Cite journal |first=A Castro |last=Neto |last2=Peres |first2=N. M. R. |last3=Novoselov |first3=K. S. |last4=Geim |first4=A. K. |last5=Geim |first5=A. K. |title=The electronic properties of graphene |journal=Rev Mod Phys |volume=81 |year=2009 |page=109 |url=http://onnes.ph.man.ac.uk/nano/Publications/RMP_2009.pdf |format=PDF |bibcode=2009RvMP...81..109C |doi=10.1103/RevModPhys.81.109 |arxiv=0709.1163 }}</ref>) | ||
| === Graphene oxide === | === Graphene oxide === | ||
| {{further2|]}} | {{further2|]}} | ||
| Using paper-making techniques on dispersed, oxidized and chemically processed graphite in water, the monolayer flakes form a single sheet and create strong bonds. These sheets, called ] have a measured ] of 32 ].<ref>{{cite web | |
Using paper-making techniques on dispersed, oxidized and chemically processed graphite in water, the monolayer flakes form a single sheet and create strong bonds. These sheets, called ] have a measured ] of 32 ].<ref>{{cite web |url=http://invo.northwestern.edu/technologies/detail/graphene-oxide-paper |archiveurl=http://web.archive.org/web/20110720013914/http://invo.northwestern.edu/technologies/detail/graphene-oxide-paper |archivedate=2011-07-20 |title=Graphene Oxide Paper |publisher=Northwestern University |accessdate=2011-02-28 }}</ref> The chemical property of graphite oxide is related to the functional groups attached to graphene sheets. These can change the polymerization pathway and similar chemical processes.<ref>{{cite journal |last=Eftekhari |first=Ali |last2=Yazdani |first2=Bahareh |title=Initiating electropolymerization on graphene sheets in graphite oxide structure |journal=Journal of Polymer Science Part A: Polymer Chemistry |volume=48 |page=2204 |year=2010 |doi=10.1002/pola.23990 |bibcode=2010JPoSA..48.2204E |issue=10 }}</ref> Graphene oxide flakes in polymers display enhanced photo-conducting properties.<ref>{{cite journal |last=Nalla |first=Venkatram |last2=Polavarapu |first2=L |last3=Manga |first3=KK |last4=Goh |first4=BM |last5=Loh |first5=KP |last6=Xu |first6=QH |last7=Ji |first7=W |title=Transient photoconductivity and femtosecond nonlinear optical properties of a conjugated polymer–graphene oxide composite |journal=Nanotechnology |volume=21 |issue=41 |page=415203 |year=2010 |pmid=20852355 |doi=10.1088/0957-4484/21/41/415203 |bibcode=2010Nanot..21O5203N }}</ref> Graphene-based membranes are impermeable to all gases and liquids (vacuum-tight). However, water evaporates through them as quickly as if the membrane was not present.<ref name="pmid22282806" /> | ||
| === Chemical modification === | === Chemical modification === | ||
| {{jargon|section|date=December 2013}} | {{jargon|section|date=December 2013}} | ||
| ] Soluble fragments of graphene can be prepared in the laboratory<ref>{{Cite journal | |
] Soluble fragments of graphene can be prepared in the laboratory<ref>{{Cite journal |first=Sandip |last=Niyogi |first2=Elena |last2=Bekyarova |first3=Mikhail E. |last3=Itkis |first4=Jared L. |last4=McWilliams |first5=Mark A. |last5=Hamon |first6=Robert C. |last6=Haddon |title=Solution Properties of Graphite and Graphene |journal=] |volume=128 |pages=7720–7721 |year=2006 |doi=10.1021/ja060680r |pmid=16771469 |issue=24 }}</ref> through chemical modification of graphite. First, microcrystalline graphite is treated with an acidic mixture of sulfuric acid and ]. A series of oxidation and exfoliation steps produce small graphene plates with ] groups at their edges. These are converted to ] groups by treatment with ]; next, they are converted to the corresponding graphene ] via treatment with ]. The resulting material (circular graphene layers of 5.3 ] thickness) is soluble in ], ] and ]. | ||
| Refluxing single-layer graphene oxide (SLGO) in ]s leads to size reduction and folding of individual sheets as well as loss of carboxylic group functionality, by up to 20%, indicating thermal instabilities of SLGO sheets dependant on their preparation methodology. When using thionyl chloride, ] groups result, which can then form aliphatic and aromatic amides with a reactivity conversion of around 70–80%. | Refluxing single-layer graphene oxide (SLGO) in ]s leads to size reduction and folding of individual sheets as well as loss of carboxylic group functionality, by up to 20%, indicating thermal instabilities of SLGO sheets dependant on their preparation methodology. When using thionyl chloride, ] groups result, which can then form aliphatic and aromatic amides with a reactivity conversion of around 70–80%. | ||
| ] | ] | ||
| ] reflux is commonly used for reducing SLGO to SLG(R), but ]s show that only around 20–30% of the carboxylic groups are lost, leaving a significant number available for chemical attachment. Analysis of SLG(R) generated by this route reveals that the system is unstable and using a room temperature stirring with HCl (< 1.0 M) leads to around 60% loss of COOH functionality. Room temperature treatment of SLGO with ]s leads to the collapse of the individual sheets into star-like clusters that exhibited poor subsequent reactivity with amines (ca. 3–5% conversion of the intermediate to the final amide).<ref>{{Cite journal | |
] reflux is commonly used for reducing SLGO to SLG(R), but ]s show that only around 20–30% of the carboxylic groups are lost, leaving a significant number available for chemical attachment. Analysis of SLG(R) generated by this route reveals that the system is unstable and using a room temperature stirring with HCl (< 1.0 M) leads to around 60% loss of COOH functionality. Room temperature treatment of SLGO with ]s leads to the collapse of the individual sheets into star-like clusters that exhibited poor subsequent reactivity with amines (ca. 3–5% conversion of the intermediate to the final amide).<ref>{{Cite journal |first=Raymond L.D. |last=Whitby |first2=Alina |last2=Korobeinyk |first3=Katya V. |last3=Glevatska |title=Morphological changes and covalent reactivity assessment of single-layer graphene oxides under carboxylic group-targeted chemistry |journal=] |volume=49 |issue=2 |pages=722–725 |year=2011 |doi=10.1016/j.carbon.2010.09.049 }}</ref> It is apparent that conventional chemical treatment of carboxylic groups on SLGO generates morphological changes of individual sheets that leads to a reduction in chemical reactivity, which may potentially limit their use in composite synthesis. Therefore, chemical reactions types have been explored. SLGO has also been grafted with ], cross-linked through ] groups. When filtered into graphene oxide paper, these composites exhibit increased stiffness and strength relative to unmodified graphene oxide paper.<ref>{{Cite journal |first=Sungjin |last=Park, |first2=Dmitriy A. |last2=Dikin |first3=SonBinh T. |last3=Nguyen |first4=Rodney S. |last4=Ruoff |title=Graphene Oxide Sheets Chemically Cross-Linked by Polyallylamine |journal=] |volume=113 |pages=15801–15804 |year=2009 |doi=10.1021/jp907613s |issue=36 }}</ref> | ||
| Full ] from both sides of graphene sheet results in ], but partial hydrogenation leads to hydrogenated graphene.<ref>{{Cite journal | |
Full ] from both sides of graphene sheet results in ], but partial hydrogenation leads to hydrogenated graphene.<ref>{{Cite journal |first=D. C. |last=Elias |last2=Nair |first2=R. R. |last3=Mohiuddin |first3=T. M. G. |last4=Morozov |first4=S. V. |last5=Blake |first5=P. |last6=Halsall |first6=M. P. |last7=Ferrari |first7=A. C. |last8=Boukhvalov |first8=D. W. |last9=Katsnelson |first9=M. I. |last10=Geim |first10=A. K. |last11=Novoselov |first11=K. S. |title=Control of Graphene's Properties by Reversible Hydrogenation: Evidence for Graphane |journal=Science |year=2009 |volume=323 |doi=10.1126/science.1167130 |pmid=19179524 |issue=5914 |bibcode=2009Sci...323..610E |pages=610–3 |arxiv=0810.4706 }}</ref> Similarly, both-side fluorination of graphene (or chemical and mechanical exfoliation of graphite fluoride) leads to ] (graphene fluoride), while partial fluorination (generally halogenation) provides fluorinated (halogenated) graphene. | ||
| === Casimir effect and dispersion === | === Casimir effect and dispersion === | ||
| The ] is an interaction between any disjoint neutral bodies provoked by the fluctuations of the electrodynamical vacuum. Mathematically it can be explained by considering the normal modes of electromagnetic fields, which explicitly depend on the boundary (or matching) conditions on the surfaces of the interacting bodies. Since the interaction of graphene with an electromagnetic field is surprisingly strong for a one-atom-thick material, the Casimir effect is of growing interest.<ref name=BFGV>{{Cite journal | |
The ] is an interaction between any disjoint neutral bodies provoked by the fluctuations of the electrodynamical vacuum. Mathematically it can be explained by considering the normal modes of electromagnetic fields, which explicitly depend on the boundary (or matching) conditions on the surfaces of the interacting bodies. Since the interaction of graphene with an electromagnetic field is surprisingly strong for a one-atom-thick material, the Casimir effect is of growing interest.<ref name=BFGV>{{Cite journal |last=Bordag |first=M. |last2=Fialkovsky |first2=I. V. |last3=Gitman |first3=D. M. |last4=Vassilevich |first4=D. V. |title=Casimir interaction between a perfect conductor and graphene described by the Dirac model |journal=Physical Review B |volume=80 |year=2009 |page=245406 |doi=10.1103/PhysRevB.80.245406 |bibcode=2009PhRvB..80x5406B |issue=24 |arxiv=0907.3242 }}</ref><ref name=FMD>{{cite journal |last=Fialkovsky |first=I. V. |last2=Marachevsky |first2=V.N. |last3=Vassilevich |first3=D. V. |title=Finite temperature Casimir effect for graphene |year=2011 |volume=84 |issue=35446 |journal=Physical Review B |arxiv=1102.1757 |bibcode=2011PhRvB..84c5446F |page=35446 |doi=10.1103/PhysRevB.84.035446 }}</ref> | ||
| The related van der Waals force (or dispersion force) is also unusual, obeying an inverse cubic, asymptotic power law in contrast to the usual inverse quartic.<ref name=DWR>{{Cite journal | |
The related van der Waals force (or dispersion force) is also unusual, obeying an inverse cubic, asymptotic power law in contrast to the usual inverse quartic.<ref name=DWR>{{Cite journal |last=Dobson |first=J. F. |last2=White |first=A. |last2=Rubio |first2=A. |title=Asymptotics of the dispersion interaction: analytic benchmarks for van der Waals energy functionals |journal=Physical Review Letters |volume=96 |year=2006 |page=073201 |doi=10.1103/PhysRevLett.96.073201 |issue=7 |bibcode=2006PhRvL..96g3201D|arxiv=cond-mat/0502422 }}</ref> | ||
| === Bilayer graphene === | === Bilayer graphene === | ||
| {{main|Bilayer graphene}} | {{main|Bilayer graphene}} | ||
| Bilayer graphene displays the ], a tunable ]<ref name="PRB75.155115">{{Cite journal |doi=10.1103/PhysRevB.75.155115 |title=Ab initio theory of gate induced gaps in graphene bilayers |year=2007 | |
Bilayer graphene displays the ], a tunable ]<ref name="PRB75.155115">{{Cite journal |doi=10.1103/PhysRevB.75.155115 |title=Ab initio theory of gate induced gaps in graphene bilayers |year=2007 |last=Min |first=Hongki |last2=Sahu |first2=Bhagawan |last3=Banerjee |first3=Sanjay |last4=MacDonald |first4=A. |journal=Physical Review B |volume=75 |issue=15|pages=155115 |arxiv=cond-mat/0612236 |bibcode=2007PhRvB..75o5115M }}</ref> and potential for ]<ref name="PRL104.096802">{{Cite journal |doi=10.1103/PhysRevLett.104.096802 |title=Anomalous Exciton Condensation in Graphene Bilayers |year=2010 |last=Barlas |first=Yafis |last2=Côté |first2=R. |last3=Lambert |first3=J. |last4=MacDonald |first4=A. H. |journal=Physical Review Letters |volume=104 |issue=9 |pages=96802 |bibcode=2010PhRvL.104i6802B|arxiv=0909.1502 }}</ref> –making them promising candidates for optoelectronic and nanoelectronic applications. Bilayer graphene typically can be found either in twisted configurations where the two layers are rotated relative to each other or graphitic Bernal stacked configurations where half the atoms in one layer lie atop half the atoms in the other. Stacking order and orientation govern the optical and electronic properties of bilayer graphene. | ||
| One way to synthesize bilayer graphene is via ], and can produce large bilayer regions that almost exclusively conform to a Bernal stack geometry.<ref name="nl204547v">{{Cite journal |doi=10.1021/nl204547v |title=Twinning and Twisting of Tri- and Bilayer Graphene |year=2012 | |
One way to synthesize bilayer graphene is via ], and can produce large bilayer regions that almost exclusively conform to a Bernal stack geometry.<ref name="nl204547v">{{Cite journal |doi=10.1021/nl204547v |title=Twinning and Twisting of Tri- and Bilayer Graphene |year=2012 |last=Min |first=Lola |last2=Hovden |first2=Robert |last3=Huang |journal=NanoLetters |volume=12 |issue=3 |first3=Pinshane |last4=Wojcik |first4=Michal |last5=Muller |first5=David A. |last6=Park |first6=Jiwoong |page=1609|bibcode=2012NanoL..12.1609B }}</ref> | ||
| === Graphene Fiber === | === Graphene Fiber === | ||
| In 2011, Xinming Li and Hongwei Zhu from Tsinghua University reported a novel yet simple approach to fabricate graphene fibers from chemical vapor deposition grown graphene films.<ref>{{Cite journal|doi=10.1021/la202380g |pmid=21875131 |title=Directly Drawing Self-Assembled, Porous, and Monolithic Graphene Fiber from Chemical Vapor Deposition Grown Graphene Film and Its Electrochemical Properties |journal=Langmuir |volume=27 |issue=19 |pages= |
In 2011, Xinming Li and Hongwei Zhu from Tsinghua University reported a novel yet simple approach to fabricate graphene fibers from chemical vapor deposition grown graphene films.<ref>{{Cite journal|doi=10.1021/la202380g |pmid=21875131 |title=Directly Drawing Self-Assembled, Porous, and Monolithic Graphene Fiber from Chemical Vapor Deposition Grown Graphene Film and Its Electrochemical Properties |journal=Langmuir |volume=27 |issue=19 |pages=12164–71 |date=29 August 2011 |last=Li |first=Xinming |last2=Zhao |first2=Tianshuo |last3=Wang |first3=Kunlin |last4=Yang |first4=Ying |last5=Wei |first5=Jinquan |last6=Kang |first6=Feiyu |last7=Wu |first7=Dehai |last8=Zhu |first8=Hongwei }}</ref> The method was scalable and controllable, delivering tunable morphology and pore structure by controlling the evaporation of solvents with suitable surface tension. Flexible all-solid-state supercapacitors based on this graphene fibers were demonstrated in 2013.<ref>{{cite web|url=http://pubs.rsc.org/en/content/articlelanding/2013/cp/c3cp52908h#!divAbstract |title=Flexible all solid-state supercapacitors based on chemical vapor deposition derived graphene fibers |date=3 September 2013 }}</ref> | ||
| === 3D graphene === | === 3D graphene === | ||
| In 2013, a three-dimensional ] of hexagonally arranged carbon was termed 3D graphene, although self-supporting 3D graphene has not yet been produced.<ref>{{Cite doi|10.1002/ange.201303497}}<br/>{{cite journal |url=http://www.kurzweilai.net/3d-graphene-could-replace-expensive-platinum-in-solar-cells |title=3D graphene could replace expensive platinum in solar cells |publisher=KurzweilAI |date= |accessdate=2013-08-24 | |
In 2013, a three-dimensional ] of hexagonally arranged carbon was termed 3D graphene, although self-supporting 3D graphene has not yet been produced.<ref>{{Cite doi|10.1002/ange.201303497}}<br/>{{cite journal |url=http://www.kurzweilai.net/3d-graphene-could-replace-expensive-platinum-in-solar-cells |title=3D graphene could replace expensive platinum in solar cells |publisher=KurzweilAI |date= |accessdate=2013-08-24 |last=Wang |first=Hui |last2=Sun |first2=Kai |last3=Tao |first3=Franklin |last4=Stacchiola |first4=Dario J. |last5=Hu |first5=Yun Hang |journal=Angewandte Chemie |volume=125 |issue=35 |page=9380 |doi=10.1002/ange.201303497 }}</ref> | ||
| == Production techniques == | == Production techniques == | ||
| Line 309: | Line 284: | ||
| Graphene planes become better separated in ] graphite compounds. | Graphene planes become better separated in ] graphite compounds. | ||
| Graphene fragments are produced (along with other debris) whenever graphite is abraded, such as when drawing with a pencil.<ref name=SciAm> | Graphene fragments are produced (along with other debris) whenever graphite is abraded, such as when drawing with a pencil.<ref name=SciAm>{{Cite news |last=Geim |first=A. K. |last2=Kim |first2=P. |date=April 2008 |title=Carbon Wonderland |url=http://www.scientificamerican.com/article.cfm?id=carbon-wonderland |work=] |quote=... bits of graphene are undoubtedly present in every pencil mark }}</ref> | ||
| {{Cite news | |||
| | last1=Geim |first1=A. K. | |||
| | last2=Kim |first2=P. | |||
| | date=April 2008 | |||
| | title=Carbon Wonderland | |||
| | url=http://www.scientificamerican.com/article.cfm?id=carbon-wonderland | |||
| | work=] | |||
| | accessdate=2009-05-05 | |||
| | quote=... bits of graphene are undoubtedly present in every pencil mark | |||
| }}</ref> | |||
| In 2011 the Institute of Electronic Materials Technology and Department of Physics at ] announced Sicilicon-based epitaxy technology for producing large pieces of graphene with the best quality to date.<ref> | In 2011 the Institute of Electronic Materials Technology and Department of Physics at ] announced Sicilicon-based epitaxy technology for producing large pieces of graphene with the best quality to date.<ref> | ||
| {{cite web |date=22 April 2011 |title=Polish scientists hope to patent graphene mass-production technology |url=http://www.wbj.pl/article-54247-polish-scientists-to-patent-graphene-mass-production-technology.html |work=] | |||
| {{cite web | |||
| }}<br/>{{cite web |last=Waszak |first=S. |date=April 2011 |title=Polish team claims leap for wonder material graphene |url=http://www.physorg.com/news/2011-04-team-material-graphene.html |work=] }}</ref> | |||
| | date=22 April 2011 | |||
| | title=Polish scientists hope to patent graphene mass-production technology | |||
| | url=http://www.wbj.pl/article-54247-polish-scientists-to-patent-graphene-mass-production-technology.html | |||
| | work=] | |||
| }}<br/> | |||
| {{cite web | |||
| | last=Waszak |first1=S. | |||
| | date=April 2011 | |||
| | title=Polish team claims leap for wonder material graphene | |||
| | url=http://www.physorg.com/news/2011-04-team-material-graphene.html | |||
| | work=] | |||
| }}</ref> | |||
| === Mechanical exfoliation === | === Mechanical exfoliation === | ||
| Line 340: | Line 294: | ||
| This involves splitting single layers of graphene from multi-layered graphite. Achieving single layers typically requires multiple exfoliation steps, each producing a slice with fewer layers, until only one remains. Geim and Novosolev used adhesive tape to split the layers. | This involves splitting single layers of graphene from multi-layered graphite. Achieving single layers typically requires multiple exfoliation steps, each producing a slice with fewer layers, until only one remains. Geim and Novosolev used adhesive tape to split the layers. | ||
| After exfoliation the flakes are deposited on a silicon wafer using "dry deposition". Individual atomic planes can be viewed with an optical microscope. Crystallites larger than 1 mm and visible to the naked eye can be obtained with the technique. It is often referred to as a "]" or "drawing" method. The latter name appeared because the dry deposition resembles drawing with a piece of graphite.<ref name="PhysTod">{{Cite journal | |
After exfoliation the flakes are deposited on a silicon wafer using "dry deposition". Individual atomic planes can be viewed with an optical microscope. Crystallites larger than 1 mm and visible to the naked eye can be obtained with the technique. It is often referred to as a "]" or "drawing" method. The latter name appeared because the dry deposition resembles drawing with a piece of graphite.<ref name="PhysTod">{{Cite journal |last=Geim |first=A. K. |last2=MacDonald |first2=A. H. |title=Graphene: Exploring carbon flatland |journal=Physics Today |volume=60 |pages=35–41 |year=2007 |doi=10.1063/1.2774096 |bibcode=2007PhT....60h..35G |issue=8 }}</ref> | ||
| === Epitaxy === | === Epitaxy === | ||
| Line 346: | Line 300: | ||
| ] refers to the deposition of a crystalline overlayer on a crystalline substrate, where there is registry between the two. In some cases epitaxial graphene layers are coupled to surfaces weakly enough (by ]s) to retain the two dimensional ] of isolated graphene.<ref name=Gall1> | ] refers to the deposition of a crystalline overlayer on a crystalline substrate, where there is registry between the two. In some cases epitaxial graphene layers are coupled to surfaces weakly enough (by ]s) to retain the two dimensional ] of isolated graphene.<ref name=Gall1> | ||
| {{cite journal | {{cite journal | ||
| | |
|last=Gall |first=N. R. | ||
| | |
|last2=Rut'Kov |first2=E. V. | ||
| | |
|last3=Tontegode |first3=A. Ya. | ||
| | |
|year=1997 | ||
| | |
|title=Two Dimensional Graphite Films on Metals and Their Intercalation | ||
| | |
|journal=] | ||
| | |
|volume=11 |issue=16 |page=1865 | ||
| | |
|bibcode=1997IJMPB..11.1865G | ||
| | |
|doi=10.1142/S0217979297000976 | ||
| }}</ref><ref name=Gall2> | }}</ref><ref name=Gall2> | ||
| {{cite journal | {{cite journal | ||
| | |
|last=Gall |first=N. R. | ||
| | |
|last2=Rut'Kov |first2=E. V. | ||
| | |
|last3=Tontegode |first3=A. Ya. | ||
| | |
|year=1995 | ||
| | |
|title=Influence of surface carbon on the formation of silicon-refractory metal interfaces | ||
| | |
|journal=] | ||
| | |
|volume=266 |issue=2 |page=229 | ||
| | |
|bibcode=1995TSF...266..229G | ||
| | |
|doi=10.1016/0040-6090(95)06572-5 | ||
| }}</ref> An example of weakly coupled epitaxial graphene is the one grown on SiC.<ref name="Nov 04"> | }}</ref> An example of weakly coupled epitaxial graphene is the one grown on SiC.<ref name="Nov 04"> | ||
| {{cite journal | {{cite journal | ||
| | |
|last=Novoselov |first=K. S. | ||
| | |
|last2=Geim |first2=A. K. | ||
| | |
|last3=Morozov |first3=S. V. | ||
| | |
|last4=Jiang |first4=D. | ||
| | |
|last5=Zhang |first5=Y. | ||
| | |
|last6=Dubonos |first6=S. V. | ||
| | |
|last7=Grigorieva |first7=I. V. | ||
| | |
|last8=Firsov |first8=A. A. | ||
| | |
|year=2004 | ||
| | |
|title=Electric Field Effect in Atomically Thin Carbon Films | ||
| | |
|url=http://onnes.ph.man.ac.uk/nano/Publications/Science_2004.pdf |format=PDF | ||
| | |
|journal=] | ||
| | |
|volume=306 |issue=5696 |pages=666–669 | ||
| | |
|arxiv=cond-mat/0410550 | ||
| | |
|bibcode=2004Sci...306..666N | ||
| | |
|doi=10.1126/science.1102896 | ||
| | |
|pmid=15499015 | ||
| }}</ref> | }}</ref> | ||
| Line 392: | Line 346: | ||
| {{Main|Tunable nanoporous carbon|l1=Carbide-derived Carbon}} | {{Main|Tunable nanoporous carbon|l1=Carbide-derived Carbon}} | ||
| Heating ] (SiC) to high temperatures (>{{val|1100|u=°C}}) under low pressures (~10<sup>−6</sup> torr) reduces it to graphene.<ref>{{Cite journal | |
Heating ] (SiC) to high temperatures (>{{val|1100|u=°C}}) under low pressures (~10<sup>−6</sup> torr) reduces it to graphene.<ref>{{Cite journal |last=Sutter |first=P. |title=Epitaxial graphene: How silicon leaves the scene |journal=Nature Materials |volume=8 |year=2009 |pmid=19229263 |doi=10.1038/nmat2392 |issue=3 |bibcode=2009NatMa...8..171S |pages=171–2 }}</ref> This process produces epitaxial graphene with dimensions dependent upon the size of the wafer. The face of the SiC used for graphene formation, silicon- or carbon-terminated, highly influences the thickness, mobility and carrier density of the resulting graphene. | ||
| The electronic band-structure (so-called Dirac cone structure) was first visualized in this material.<ref name=ohta1>{{Cite journal | |
The electronic band-structure (so-called Dirac cone structure) was first visualized in this material.<ref name=ohta1>{{Cite journal |last=Ohta, |first=T. |year=2007 |title=Interlayer Interaction and Electronic Screening in Multilayer Graphene Investigated with Angle-Resolved Photoemission Spectroscopy |journal=Physical Review Letters |volume=98 |page=206802 |doi=10.1103/PhysRevLett.98.206802 |pmid=17677726 |bibcode=2007PhRvL..98t6802O |issue=20 |last2=Bostwick |first2=Aaron |last3=McChesney |first3=J. |last4=Seyller |first4=Thomas |last5=Horn |first5=Karsten |last6=Rotenberg |first6=Eli }}</ref><ref name=ohta2>{{Cite journal |last=Bostwick |first=A. |year=2007 |title=Symmetry breaking in few layer graphene films |journal=New Journal of Physics |volume=9 |page=385 |doi=10.1088/1367-2630/9/10/385 |bibcode=2007NJPh....9..385B |issue=10 |last2=Ohta |first2=Taisuke |last3=McChesney |first3=Jessica L |last4=Emtsev |first4=Konstantin V |last5=Seyller |first5=Thomas |last6=Horn |first6=Karsten |last7=Rotenberg |first7=Eli |arxiv=0705.3705 }}</ref><ref name="Lanzara06">{{Cite journal |last=Zhou |first=S.Y. |last2=Gweon |first2=G.-H. |last3=Graf |first3=J. |last4=Fedorov |first4=A. V. |last5=Spataru |first5=C. D. |last6=Diehl |first6=R. D. |last7=Kopelevich |first7=Y. |last8=Lee |first8=D.-H. |last9=Louie |first9=Steven G. |last10=Lanzara |first10=A. |title=First direct observation of Dirac fermions in graphite |doi=10.1038/nphys393 |journal=Nature Physics |volume=2 |pages=595–599 |year=2006 |arxiv=cond-mat/0608069 |bibcode=2006NatPh...2..595Z |issue=9 }}</ref> Weak anti-localization is observed in this material, but not in exfoliated graphene produced by the pencil-trace method.<ref name=exf>{{Cite journal |last=Morozov |first=S.V. |title=Strong Suppression of Weak Localization in Graphene |doi=10.1103/PhysRevLett.97.016801 |journal=Physical Review Letters |volume=97 |page=016801 |year=2006 |pmid=16907394 |issue=1 |bibcode=2006PhRvL..97a6801M |arxiv=cond-mat/0603826 |last2=Novoselov |first2=K. S. |last3=Katsnelson |first3=M. I. |last4=Schedin |first4=F. |last5=Ponomarenko |first5=L. A. |last6=Jiang |first6=D. |last7=Geim |first7=A. K. }}</ref> Large, temperature-independent mobilities have been observed, approaching those in exfoliated graphene placed on silicon oxide, but lower than mobilities in suspended graphene produced by the drawing method. Even without transfer, graphene on SiC exhibits massless Dirac fermions.<ref name="ByungHeeHong"/><ref name="0908.1900">{{cite journal |first=Johannes |last=Jobst |first2=Daniel |last2=Waldmann |first3=Florian |last3=Speck |first4=Roland |last4=Hirner |first5=Duncan K. |last5=Maude |first6=Thomas |last6=Seyller |first7=Heiko B. |last7=Weber |title=How Graphene-like is Epitaxial Graphene? Quantum Oscillations and Quantum Hall Effect |year=2009 |doi=10.1103/PhysRevB.81.195434 |journal=Physical Review B |volume=81 |issue=19 |pages=195434 |arxiv=0908.1900|bibcode=2010PhRvB..81s5434J }}</ref><ref name="ShenAPL">{{Cite journal |first=T. |last=Shen |first2=J.J. |last2=Gu |first3=M |last3=Xu |first4=Y.Q. |last4=Wu |first5=M.L. |last5=Bolen |first6=M.A. |last6=Capano |first7=L.W. |last7=Engel |first8=P.D. |last8=Ye |title=Observation of quantum-Hall effect in gated epitaxial graphene grown on SiC (0001) |doi=10.1063/1.3254329 |journal=Applied Physics Letters |bibcode=2009ApPhL..95q2105S |year=2009 |volume=95 |issue=17 |page=172105 |arxiv=0908.3822 }}</ref><ref name=0909.2903>{{cite journal |first=Xiaosong |last=Wu, |first2=Yike |last2=Hu |first3=Ming |last3=Ruan |first4=Nerasoa K |last4=Madiomanana |first5=John |last5=Hankinson |first6=Mike |last6=Sprinkle |first7=Claire |last7=Berger |first8=Walt A. |last8=de Heer |year=2009 |title=Half integer quantum Hall effect in high mobility single layer epitaxial graphene |doi=10.1063/1.3266524 |journal=Applied Physics Letters |volume=95 |issue=22 |page=223108 |arxiv=0909.2903|bibcode=2009ApPhL..95v3108W }}</ref><ref name=0909.1193>{{cite journal |first=Samuel |last=Lara-Avila |first2=Alexei |last2=Kalaboukhov |first3=Sara |last3=Paolillo |first4=Mikael |last4=Syväjärvi |first5=Rositza |last5=Yakimova |first6=Vladimir |last6=Fal'ko |first7=Alexander |last7=Tzalenchuk |first8=Sergey |last8=Kubatkin |year=2009 |title=SiC Graphene Suitable For Quantum Hall Resistance Metrology |doi=10.1038/nnano.2009.474 |journal=Nature Nanotechnology |volume=5 |issue=3 |pages=186–9 |pmid=20081845 |arxiv=0909.1193 |bibcode=2010NatNa...5..186T }}<!-- sources differ --></ref><ref name=phase1>{{cite journal |first=J.A. |last=Alexander-Webber |first2=A.M.R. |last2=Baker |first3=T.J.B.M. |last3=Janssen |first4=A. |last4=Tzalenchuk |first5=S. |last5=Lara-Avila |first6=S. |last6=Kubatkin |first7=R. |last7=Yakimova |first8=B. A. |last8=Piot |first9=D. K. |last9=Maude |first10=R.J. |last10=Nicholas |year=2013 |title=Phase Space for the Breakdown of the Quantum Hall Effect in Epitaxial Graphene |doi=10.1103/PhysRevLett.111.096601 |journal=Physical Review Letters |volume=111 |issue=9 |page=096601 |pmid=24033057 |arxiv=1304.4897|bibcode=2013PhRvL.111i6601A }}</ref> | ||
| The weak van der Waals force that provides the cohesion of multilayer graphene stacks does not always affect the electronic properties of the individual graphene layers in the stack. That is, while the electronic properties of certain multilayered epitaxial graphenes are identical to that of a single layer,<ref name="Hass1">{{Cite journal | |
The weak van der Waals force that provides the cohesion of multilayer graphene stacks does not always affect the electronic properties of the individual graphene layers in the stack. That is, while the electronic properties of certain multilayered epitaxial graphenes are identical to that of a single layer,<ref name="Hass1">{{Cite journal |last=Hass |first=J. |year=2008 |title=Why multilayer graphene on 4H-SiC(000(1)over-bar) behaves like a single sheet of graphene |journal=Physical Review Letters |volume=100 |page=125504 |doi=10.1103/PhysRevLett.100.125504 |bibcode=2008PhRvL.100l5504H |issue=12 |last2=Varchon |first2=F. |last3=Millán-Otoya |first3=J. |last4=Sprinkle |first4=M. |last5=Sharma |first5=N. |last6=De Heer |first6=W. |last7=Berger |first7=C. |last8=First |first8=P. |last9=Magaud |first9=L. |last10=Conrad |first10=E. }}</ref> in other cases the properties are affected,<ref name=ohta1/><ref name=ohta2/> as they are in bulk graphite. This effect is well understood theoretically and is related to the symmetry of the interlayer interactions.<ref name="Hass1"/> | ||
| Epitaxial graphene on SiC can be patterned using standard microelectronics methods. The band gap can be tuned by laser irradiation.<ref>{{cite journal |doi=10.1021/nn201757j |title=Laser Patterning of Epitaxial Graphene for Schottky Junction Photodetectors |year=2011 | |
Epitaxial graphene on SiC can be patterned using standard microelectronics methods. The band gap can be tuned by laser irradiation.<ref>{{cite journal |doi=10.1021/nn201757j |title=Laser Patterning of Epitaxial Graphene for Schottky Junction Photodetectors |year=2011 |last=Singh |first=Ram Sevak |last2=Nalla |first2=Venkatram |last3=Chen |first3=Wei |last4=Wee |first4=Andrew Thye Shen |last5=Ji |first5=Wei |journal=ACS Nano |volume=5 |issue=7 |pages=5969–75 |pmid=21702443 }}</ref> | ||
| ==== Metal substrates ==== | ==== Metal substrates ==== | ||
| The atomic structure of a metal substrate can seed the growth of graphene. Graphene grown on ] does not typically produce uniform layer thickness. Bonding between the bottom graphene layer and the substrate may affect layer properties.<ref name |
The atomic structure of a metal substrate can seed the growth of graphene. Graphene grown on ] does not typically produce uniform layer thickness. Bonding between the bottom graphene layer and the substrate may affect layer properties.<ref name="PhysOrg.com">{{Cite news |title=A smarter way to grow graphene |url=http://www.physorg.com/news129980833.html |publisher=PhysOrg.com |date=May 2008 }}</ref> | ||
| Graphene grown on ] is very weakly bonded, uniform in thickness and can be highly ordered. As on many other substrates, graphene on iridium is slightly rippled. Due to the long-range order of these ripples, minigaps in the electronic band-structure (Dirac cone) become visible.<ref name="grIr111">{{Cite journal | |
Graphene grown on ] is very weakly bonded, uniform in thickness and can be highly ordered. As on many other substrates, graphene on iridium is slightly rippled. Due to the long-range order of these ripples, minigaps in the electronic band-structure (Dirac cone) become visible.<ref name="grIr111">{{Cite journal |last=Pletikosić |first=I. |year=2009 |title=Dirac Cones and Minigaps for Graphene on Ir(111) |journal=Physical Review Letters |volume=102 |page=056808 |doi=10.1103/PhysRevLett.102.056808 |bibcode=2009PhRvL.102e6808P |issue=5 |last2=Kralj |first2=M. |last3=Pervan |first3=P. |last4=Brako |first4=R. |last5=Coraux |first5=J. |last6=n’Diaye |first6=A. |last7=Busse |first7=C. |last8=Michely |first8=T. |arxiv=0807.2770 }}</ref> | ||
| High-quality sheets of few-layer graphene exceeding {{convert|1|cm2|abbr=on|sigfig=1}} in area have been synthesized via ] on thin ] films with ] as a carbon source. These sheets have been successfully transferred to various substrates.<ref name="ByungHeeHong">{{Cite journal |last |
High-quality sheets of few-layer graphene exceeding {{convert|1|cm2|abbr=on|sigfig=1}} in area have been synthesized via ] on thin ] films with ] as a carbon source. These sheets have been successfully transferred to various substrates.<ref name="ByungHeeHong">{{Cite journal |last=Kim |first=Kuen Soo |author2=''et al.'' |title=Large-scale pattern growth of graphene films for stretchable transparent electrodes |year=2009 |doi=10.1038/nature07719 |journal=Nature |volume=457 |pmid=19145232 |issue=7230 |bibcode=2009Natur.457..706K |pages=706–10 }}</ref><ref name="hongR" /><ref>{{cite journal |first=J. |last=Rafiee |first2=X. |last2=Mi |first3=H. |last3=Gullapalli |first4=A.V. |last4=Thomas |first5=F. |last5=Yavari |first6=Y. |last6=Shi |first7=P.M. |last7=Ajayan |first8=N.A. |last8=Koratkar |title=Wetting transparency of graphene |journal=Nature Materials |issue=11 |year=2012 |pages=217-222 }}</ref> | ||
| An improvement of this technique employs ] foil; at very low pressure, the growth of graphene automatically stops after a single graphene layer forms. Arbitrarily large films can be created.<ref name |
An improvement of this technique employs ] foil; at very low pressure, the growth of graphene automatically stops after a single graphene layer forms. Arbitrarily large films can be created.<ref name=hongR/><ref name="CopperGraphene">{{Cite journal |last=Li |first=Xuesong |author2=''et al.'' |title=Large-Area Synthesis of High-Quality and Uniform Graphene Films on Copper Foils |year=2009 |pmid=19423775 |doi=10.1126/science.1171245 |journal=Science |volume=324 |issue=5932 |bibcode=2009Sci...324.1312L |pages=1312–4 |arxiv=0905.1712 }}</ref> The single layer growth is also due to low concentration of carbon in methane. Larger ]s such as ] and ] produce bilayer graphene.<ref>{{cite journal |last=Wassei |first=Jonathan K. |last2=Mecklenburg |first2=Matthew |last3=Torres |first3=Jaime A.|last4=Fowler |first4=Jesse D. |last5=Regan |first5=B. C. |last6=Kaner |first6=Richard B. |last7=Weiller |first7=Bruce H. |title=Chemical Vapor Deposition of Graphene on Copper from Methane, Ethane and Propane: Evidence for Bilayer Selectivity |journal=Small |date=12 May 2012 |volume=8 |issue=9 |pages=1415–1422 |doi=10.1002/smll.201102276 |pmid=22351509 }}</ref> Atmospheric pressure CVD growth produces multilayer graphene on copper (similar to that grown on nickel films).<ref name=lenski>{{cite journal |last=Lenski |first=Daniel R. |last2=Fuhrer |first2=Michael S. |title=Raman and optical characterization of multilayer turbostratic graphene grown via chemical vapor deposition |year=2011 |doi=10.1063/1.3605545 |journal=Journal of Applied Physics |volume=110 |page=013720 |arxiv=1011.1683 |bibcode=2011JAP...110a3720L }}</ref> Graphene has been demonstrated at temperatures compatible with conventional ] processing, using a nickel-based alloy with gold as catalyst.<ref name="cmosgraphene">{{Cite journal |last=Weatherup |first=R.S. |year=2011 |title=In Situ Characterization of Alloy Catalysts for Low-Temperature Graphene Growth |journal=Nano Letters |doi=10.1021/nl202036y |volume=11 |issue=10 |pages=4154–60 |pmid=21905732 |last2=Bayer |first2=Bernhard C. |last3=Blume |first3=Raoul |last4=Ducati |first4=Caterina |last5=Baehtz |first5=Carsten |last6=Schlögl |first6=Robert |last7=Hofmann |first7=Stephan |bibcode=2011NanoL..11.4154W }}</ref> | ||
| === Reduction of graphite oxide === | === Reduction of graphite oxide === | ||
| ] reduction was probably the first method of graphene synthesis. P. Boehm reported producing monolayer flakes of reduced graphene oxide in 1962.<ref name="Boehm">. Graphene Times (2009-12-07). Retrieved on 2010-12-10.</ref> Geim acknowledged Boehm's contribution.<ref>. Aps.org. January 2010.</ref> Rapid heating of graphite oxide and exfoliation yields highly dispersed carbon powder with a few percent of graphene flakes. Reduction of graphite oxide monolayer films, e.g. by ], ] in ]/], was reported to yield graphene films. However, the quality is lower compared to scotch-tape graphene, due to incomplete removal of functional groups. Furthermore, the ] protocol introduces permanent defects due to over-oxidation. Recently, the oxidation protocol was enhanced to yield ] with an almost intact carbon framework that allows highly efficient removal of functional groups. The measured ] mobility exceeded {{convert|1000|cm|2}}/Vs.<ref name="Eigler2013">{{cite journal | |
] reduction was probably the first method of graphene synthesis. P. Boehm reported producing monolayer flakes of reduced graphene oxide in 1962.<ref name="Boehm">. Graphene Times (2009-12-07). Retrieved on 2010-12-10.</ref> Geim acknowledged Boehm's contribution.<ref>. Aps.org. January 2010.</ref> Rapid heating of graphite oxide and exfoliation yields highly dispersed carbon powder with a few percent of graphene flakes. Reduction of graphite oxide monolayer films, e.g. by ], ] in ]/], was reported to yield graphene films. However, the quality is lower compared to scotch-tape graphene, due to incomplete removal of functional groups. Furthermore, the ] protocol introduces permanent defects due to over-oxidation. Recently, the oxidation protocol was enhanced to yield ] with an almost intact carbon framework that allows highly efficient removal of functional groups. The measured ] mobility exceeded {{convert|1000|cm|2}}/Vs.<ref name="Eigler2013">{{cite journal |first=S. |last=Eigler |first2=M. |last2=Enzelberger-Heim |first3=S. |last3=Grimm |first4=P. |last=Hofmann |first=W. |last=Kroener |first=A. |last=Geworski |first=C. |last=Dotzer |first4=M. |last5=Röckert |first5=J. |last5=Xiao |first6=C. |last6=Papp |first7=O. |last7=Lytken |first8=H.-P. |last8=Steinrück |first9=P. |last9=Müller |first10=A. |last10=Hirsch |title=Wet Chemical Synthesis of Graphene |journal=Advanced Materials |volume=25 |issue=26 |year=2013 |pages=3583–3587 |doi=10.1002/adma.201300155 |pmid=23703794 }}</ref> ] analysis of reduced graphene oxide has been conducted.<ref name="Yamada">{{cite doi|10.1007/s10853-013-7630-0 }}</ref><ref>{{cite doi|10.1039/C2CP40790F }}</ref> | ||
| Applying a layer of graphite oxide film to a ] and burning it in a DVD writer produced a thin graphene film with high electrical conductivity (1738 siemens per meter) and specific surface area (1520 square meters per gram), and was highly resistant and malleable.<ref>{{cite web |url=http://www.sciencemag.org/content/335/6074/1326 |title=Laser Scribing of High-Performance and Flexible Graphene-Based Electrochemical Capacitors |publisher=Sciencemag.org |date= |
Applying a layer of graphite oxide film to a ] and burning it in a DVD writer produced a thin graphene film with high electrical conductivity (1738 siemens per meter) and specific surface area (1520 square meters per gram), and was highly resistant and malleable.<ref>{{cite web |url=http://www.sciencemag.org/content/335/6074/1326 |title=Laser Scribing of High-Performance and Flexible Graphene-Based Electrochemical Capacitors |publisher=Sciencemag.org |date=16 March 2012 }}<br/>{{cite web |last=Marcus |first=Jennifer |url=http://newsroom.ucla.edu/portal/ucla/ucla-researchers-develop-new-graphene-230478.aspx |title=Researchers develop graphene supercapacitor holding promise for portable electronics / UCLA Newsroom |publisher=Newsroom.ucla.edu |date=15 March 2012 }}</ref> | ||
| === Metal-carbon melts === | === Metal-carbon melts === | ||
| This process dissolves carbon atoms inside a ] melt at a certain temperature and then precipitates the dissolved carbon at lower temperatures as single layer graphene (SLG).<ref name="shaahin">{{Cite journal | |
This process dissolves carbon atoms inside a ] melt at a certain temperature and then precipitates the dissolved carbon at lower temperatures as single layer graphene (SLG).<ref name="shaahin">{{Cite journal |first=Shaahin |last=Amini |first2=Javier |last2=Garay |first3=Guanxiong |last3=Liu |first4=Alexander A. |last4=Balandin |first5=Reza |last5=Abbaschian |title=Growth of Large-Area Graphene Films from Metal-Carbon Melts |journal=Journal of Applied Physics |volume=108 |issue=9 |page=094321 |year=2010 |doi=10.1063/1.3498815 |bibcode=2010JAP...108i4321A |arxiv=1011.4081 }}</ref> | ||
| The metal is first melted in contact with a carbon source, possibly a graphite crucible inside which the melt is carried out or graphite powder or chunks that are placed in the melt. Keeping the melt in contact with the carbon at a specific temperature dissolves the carbon atoms, saturating the melt based on the ] of metal-carbon. Upon lowering the temperature, carbon's solubility decreases and the excess carbon precipitates atop the melt. The floating layer can be either skimmed or frozen for later removal. Using different morphology, including thick graphite, few layer graphene (FLG) and SLG were observed on metal substrate. ] proved that SLG had grown on ] substrate. The SLG Raman spectrum featured no D and D′ band, indicating its pristine nature. Among transition metals, nickel provides the best substrate for growing SLG. Since nickel is not Raman active, direct Raman spectroscopy of graphene layers on top of the nickel is achievable.<ref name="shaahin"/> | The metal is first melted in contact with a carbon source, possibly a graphite crucible inside which the melt is carried out or graphite powder or chunks that are placed in the melt. Keeping the melt in contact with the carbon at a specific temperature dissolves the carbon atoms, saturating the melt based on the ] of metal-carbon. Upon lowering the temperature, carbon's solubility decreases and the excess carbon precipitates atop the melt. The floating layer can be either skimmed or frozen for later removal. Using different morphology, including thick graphite, few layer graphene (FLG) and SLG were observed on metal substrate. ] proved that SLG had grown on ] substrate. The SLG Raman spectrum featured no D and D′ band, indicating its pristine nature. Among transition metals, nickel provides the best substrate for growing SLG. Since nickel is not Raman active, direct Raman spectroscopy of graphene layers on top of the nickel is achievable.<ref name="shaahin"/> | ||
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| === Sodium ethoxide pyrolysis === | === Sodium ethoxide pyrolysis === | ||
| Gram-quantities of graphene were produced by the reduction of ] by ] metal, followed by ] of the ] product and washing with water to remove sodium salts.<ref>{{Cite journal |doi |
Gram-quantities of graphene were produced by the reduction of ] by ] metal, followed by ] of the ] product and washing with water to remove sodium salts.<ref>{{Cite journal |doi=10.1038/nnano.2008.365 |title=Gram-scale production of graphene based on solvothermal synthesis and sonication |year=2008 |last=Choucair |first=M. |journal=Nature Nanotechnology |pmid=19119279 |volume=4 |issue=1 |pages=30–3 |last2=Thordarson |first2=P |last3=Stride |first3=JA |bibcode=2009NatNa...4...30C }}</ref> | ||
| === Nanotube slicing === | === Nanotube slicing === | ||
| Graphene can be created by cutting open ]s.<ref>{{cite journal | |
Graphene can be created by cutting open ]s.<ref>{{cite journal |title=Nanotubes cut to ribbons New techniques open up carbon tubes to create ribbons |last=Brumfiel |first=G. |journal=Nature |year=2009 |doi=10.1038/news.2009.367 }}</ref> In one such method ] are cut open in solution by action of ] and ].<ref>{{Cite journal |title=Longitudinal unzipping of carbon nanotubes to form graphene nanoribbons |last=Kosynkin |first=D. V. |journal=Nature |volume=458 |year=2009 |doi=10.1038/nature07872 |pmid=19370030 |issue=7240 |bibcode=2009Natur.458..872K |pages=872–6 |last2=Higginbotham |first2=Amanda L. |last3=Sinitskii |first3=Alexander |last4=Lomeda |first4=Jay R. |last5=Dimiev |first5=Ayrat |last6=Price |first6=B. Katherine |last7=Tour |first7=James M. }}</ref> In another method graphene nanoribbons were produced by ] of nanotubes partly embedded in a ] film.<ref>{{Cite journal |title=Narrow graphene nanoribbons from carbon nanotubes |last=Liying |first=Jiao |first2=Li |last2=Zhang |first3=Xinran |last3=Wang |first4=Georgi |last4=Diankov |first5=Hongjie |last5=Dai |authorlink5=Hongjie Dai |journal=Nature |volume=458 |year=2009 |doi=10.1038/nature07919 |pmid=19370031 |issue=7240 |bibcode=2009Natur.458..877J |pages=877–80 }}</ref> | ||
| === Solvent exfoliation === | === Solvent exfoliation === | ||
| Dispersing graphite in a proper liquid medium can produce graphene by ]. Non-exfoliated graphite is separated from graphene by ],<ref>{{cite doi|10.1038/nnano.2008.215}}</ref> producing graphene concentrations initially up to {{val|0.01|u=mg/ml}} in ] (NMP) and later to {{val|2.1|u=mg/ml}} in NMP,.<ref>{{cite doi|10.1039/C1JM11076D}}</ref> Using a suitable ] as the dispersing liquid medium for graphite exfoliation<ref>{{cite doi|10.1039/C0JM02461A}}</ref> produced concentrations of {{val|5.33|u=mg/ml}}. The concentration of graphene sheets produced by this method is very low because there is nothing preventing the sheets from restacking due to the van der Waals forces pulling them back together. the maximum concentrations achieved are the points at which the van der Waals forces overcome the interactive forces between the graphene sheets and the solvent molecules. | Dispersing graphite in a proper liquid medium can produce graphene by ]. Non-exfoliated graphite is separated from graphene by ],<ref>{{cite doi|10.1038/nnano.2008.215 }}</ref> producing graphene concentrations initially up to {{val|0.01|u=mg/ml}} in ] (NMP) and later to {{val|2.1|u=mg/ml}} in NMP,.<ref>{{cite doi|10.1039/C1JM11076D }}</ref> Using a suitable ] as the dispersing liquid medium for graphite exfoliation<ref>{{cite doi|10.1039/C0JM02461A }}</ref> produced concentrations of {{val|5.33|u=mg/ml}}. The concentration of graphene sheets produced by this method is very low because there is nothing preventing the sheets from restacking due to the van der Waals forces pulling them back together. the maximum concentrations achieved are the points at which the van der Waals forces overcome the interactive forces between the graphene sheets and the solvent molecules. | ||
| === Surfactant-aided exfoliation === | === Surfactant-aided exfoliation === | ||
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| === Interface trapping === | === Interface trapping === | ||
| Macro-scale graphene films can be created by sonicating graphite while at the interface of two immiscible liquids, most notably heptane and water. The graphene sheets are exfoliated because of the sonication and then adsorbed to the high energy interface between the heptane and the water, where they are kept from restacking. The force holding the graphene at the interface is very strong, withstanding forces in excess of 300,000 g. The solvents may then be evaporated, leaving behind the graphene film. Films created using the interface trapping method are very transparent (up to ~95 %T) and conductive.<ref>Woltornist, S. J., Oyer, A. J., Carrillo, J.-M. Y., Dobrynin, A. V, & Adamson, D. H. (2013). Conductive thin films of pristine graphene by solvent interface trapping. ACS nano, 7(8), 7062–6. {{DOI|10.1021/nn402371c}}</ref> | Macro-scale graphene films can be created by sonicating graphite while at the interface of two immiscible liquids, most notably heptane and water. The graphene sheets are exfoliated because of the sonication and then adsorbed to the high energy interface between the heptane and the water, where they are kept from restacking. The force holding the graphene at the interface is very strong, withstanding forces in excess of 300,000 g. The solvents may then be evaporated, leaving behind the graphene film. Films created using the interface trapping method are very transparent (up to ~95 %T) and conductive.<ref>Woltornist, S. J., Oyer, A. J., Carrillo, J.-M. Y., Dobrynin, A. V, & Adamson, D. H. (2013). Conductive thin films of pristine graphene by solvent interface trapping. ACS nano, 7(8), 7062–6. {{DOI|10.1021/nn402371c }}</ref> | ||
| === Carbon dioxide reduction === | === Carbon dioxide reduction === | ||
| A highly exothermic reaction combusts ] in an oxidation-reduction reaction with carbon dioxide, producing a variety of carbon nanoparticles including graphene and ]s. The carbon dioxide reactant may be either solid (dry-ice) or gaseous. The products of this reaction are carbon and ]. {{cite patent|US|8377408|status=patent}} was issued for this process.<ref>{{cite doi|10.1039/C1JM11227A}}</ref> | A highly exothermic reaction combusts ] in an oxidation-reduction reaction with carbon dioxide, producing a variety of carbon nanoparticles including graphene and ]s. The carbon dioxide reactant may be either solid (dry-ice) or gaseous. The products of this reaction are carbon and ]. {{cite patent|US|8377408|status=patent}} was issued for this process.<ref>{{cite doi|10.1039/C1JM11227A }}</ref> | ||
| == Potential applications == | == Potential applications == | ||
| Potential applications include lightweight, thin, flexible, yet durable display screens, electric circuits, and solar cells, as well as various medical, chemical and industrial processes enhanced or enabled by the use of new graphene materials.<ref>{{cite web |last=Monie |first=Sanjay |title=Developments in Conductive Inks |url=http://industrial-printing.net/content/developments-conductive-inks?page=0%2C3 |
Potential applications include lightweight, thin, flexible, yet durable display screens, electric circuits, and solar cells, as well as various medical, chemical and industrial processes enhanced or enabled by the use of new graphene materials.<ref>{{cite web |last=Monie |first=Sanjay |title=Developments in Conductive Inks |url=http://industrial-printing.net/content/developments-conductive-inks?page=0%2C3 |publisher=Industrial & Specialty Printing |accessdate=2010-04-26 }}</ref> | ||
| In 2008, graphene produced by exfoliation was one of the most expensive materials on Earth, with a sample with the area of the cross section of a human hair costing more than $1,000 as of April 2008 (about $100,000,000/cm<sup>2</sup>).<ref name |
In 2008, graphene produced by exfoliation was one of the most expensive materials on Earth, with a sample with the area of the cross section of a human hair costing more than $1,000 as of April 2008 (about $100,000,000/cm<sup>2</sup>).<ref name=SciAm/> Since then, exfoliation procedures have been scaled up, and now companies sell graphene in large quantities.<ref> | ||
| {{cite journal | {{cite journal | ||
| | |
|last=Segal |first=M. | ||
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|year=2009 | ||
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|title=Selling graphene by the ton | ||
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|journal=] | ||
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|volume=4 |issue=10 |pages=612–4 | ||
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|bibcode=2009NatNa...4..612S | ||
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| }}</ref> The price of epitaxial graphene on SiC is dominated by the substrate price, which was approximately $100/cm<sup>2</sup> as of 2009.{{update|date=December 2013}} Hong and his team in South Korea pioneered the synthesis of large-scale graphene films using ] (CVD) on thin ] layers, which triggered research on practical applications,<ref> | }}</ref> The price of epitaxial graphene on SiC is dominated by the substrate price, which was approximately $100/cm<sup>2</sup> as of 2009.{{update|date=December 2013}} Hong and his team in South Korea pioneered the synthesis of large-scale graphene films using ] (CVD) on thin ] layers, which triggered research on practical applications,<ref> | ||
| {{cite web | {{cite web | ||
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| }}</ref> with wafer sizes up to {{convert|30|in}} reported.<ref name=hongR> | }}</ref> with wafer sizes up to {{convert|30|in}} reported.<ref name=hongR> | ||
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|volume=5 |issue=8 |pages=574–578 | ||
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| In 2013, the European Union made a €1 billion grant to be used for research into potential graphene applications.<ref>{{cite web |url=http://europa.eu/rapid/press-release_IP-13-54_en.htm |title=EUROPA - PRESS RELEASES - Press Release - Graphene and Human Brain Project win largest research excellence award in history, as battle for sustained science funding continues |publisher=Europa.eu |date= |
In 2013, the European Union made a €1 billion grant to be used for research into potential graphene applications.<ref>{{cite web |url=http://europa.eu/rapid/press-release_IP-13-54_en.htm |title=EUROPA - PRESS RELEASES - Press Release - Graphene and Human Brain Project win largest research excellence award in history, as battle for sustained science funding continues |publisher=Europa.eu |date=28 January 2013 }}</ref> In 2013 the ] consortium formed, including ] and seven other European universities and research centers, along with ].<ref>{{cite web |last=Thomson |first=Iain |title=Nokia shares $1.35bn EU graphene research grant |url=http://www.theregister.co.uk/2013/02/01/nokia_eu_graphene_grant/ |publisher=The Register}}<br/>{{cite web |url=http://www.graphene-flagship.eu/GF/consortium.php |title=FET Graphene Flagship |publisher=Graphene-flagship.eu |date= |accessdate=2013-08-24 }}</ref> ] has also been working on graphene technology for several years.<ref>{{cite web |last=Sherriff |first=Lucy |url=http://www.zdnet.com/nokia-dials-into-graphene-in-photo-sensor-patent-move-7000003759/ |title=Nokia dials into graphene in photo-sensor patent move |publisher=ZDNet |date=5 September 2012 }}</ref> | ||
| === Medicine === | === Medicine === | ||
| Graphene is reported to have enhanced ] by increasing the yield of ] product.<ref name="doi10.1088/0957-4484/23/45/455106">{{cite doi|10.1088/0957-4484/23/45/455106}}</ref> Experiments revealed that graphene's ] could be the main factor behind this result. Graphene yields DNA product equivalent to positive control with up to 65% reduction in PCR cycles. | Graphene is reported to have enhanced ] by increasing the yield of ] product.<ref name="doi10.1088/0957-4484/23/45/455106">{{cite doi|10.1088/0957-4484/23/45/455106 }}</ref> Experiments revealed that graphene's ] could be the main factor behind this result. Graphene yields DNA product equivalent to positive control with up to 65% reduction in PCR cycles. | ||
| === Integrated circuits === | === Integrated circuits === | ||
| For ], graphene has a high ], as well as low noise, allowing it to be used as the channel in a ]. Single sheets of graphene are hard to produce and even harder to make on an appropriate substrate.<ref>{{Cite journal | |
For ], graphene has a high ], as well as low noise, allowing it to be used as the channel in a ]. Single sheets of graphene are hard to produce and even harder to make on an appropriate substrate.<ref>{{Cite journal |last=Chen |first=J. |last2=Ishigami |first2=M. |last3=Jang |first3=C. |last4=Hines |first4=D. R. |last5=Fuhrer |first5=M. S. |last6=Williams |first6=E. D. |title=Printed graphene circuits |journal=Advanced Materials |volume=19 |pages=3623–3627 |year=2007 |doi=10.1002/adma.200701059 |issue=21 }}</ref> | ||
| In 2008, the smallest transistor so far, one atom thick, 10 atoms wide was made of graphene.<ref name=" |
In 2008, the smallest transistor so far, one atom thick, 10 atoms wide was made of graphene.<ref name="Ponomarenko_2008_356" /> IBM announced in December 2008 that they had fabricated and characterized graphene transistors operating at GHz frequencies.<ref>{{cite web |url=http://arxivblog.com/?p=755 |title=Graphene transistors clocked at 26 GHz Arxiv article |publisher=Arxivblog.com |date=11 December 2008 }}</ref> In May 2009, an n-type transistor was announced meaning that both n and p-type graphene transistors had been created.<ref>{{Cite journal |laysummary=http://news.ufl.edu/2009/05/07/graphene/ |journal=Science |volume=324 |issue=5928 |year=2009 |pmid=19423822 |doi=10.1126/science.1170335 |title=N-Doping of Graphene Through Electrothermal Reactions with Ammonia |bibcode=2009Sci...324..768W |pages=768–71 |author-separator=; |last=Wang |first=X. |last2=Li |first2=X. |last3=Zhang |first3=L. |last4=Yoon |first4=Y. |last5=Weber |first5=P. K. |last6=Wang |first6=H. |last7=Guo |first7=J. |last8=Dai |first8=H. |authorlink8=Hongjie Dai }}</ref><ref name="americanelements">{{cite web |title=Nanotechnology Information Center: Properties, Applications, Research, and Safety Guidelines |url=http://www.americanelements.com/nanotech.htm |publisher=] }}</ref> A functional graphene integrated circuit was demonstrated – a complementary ] consisting of one p- and one n-type graphene transistor.<ref>{{Cite journal |laysummary=http://physicsworld.com/cws/article/news/38924 |last=Traversi |first=F. |last2=Russo |first2=V. |last3=Sordan |first3=R. |journal=Appl. Phys. Lett. |volume=94 |page=223312 |year=2009 |doi=10.1063/1.3148342 |title=Integrated complementary graphene inverter |bibcode=2009ApPhL..94v3312T |issue=22 |arxiv=0904.2745 }}</ref> However, this inverter suffered from a very low voltage gain. | ||
| According to a January 2010 report,<ref name="UK's NPL">{{cite web |url |
According to a January 2010 report,<ref name="UK's NPL">{{cite web |url=http://www.npl.co.uk/news/european-collaboration-breakthrough-in-developing-graphene |title=European collaboration breakthrough in developing graphene |publisher=NPL |date=19 January 2010 }}</ref> graphene was epitaxially grown on SiC in a quantity and with quality suitable for mass production of integrated circuits. At high temperatures, the quantum Hall effect could be measured in these samples. IBM built 'processors' using 100 GHz transistors on {{convert|2|in|mm|adj=on}} graphene sheets.<ref name="LinDimitrakopoulos2010">{{cite journal |last=Lin |first=Y.-M. |last2=Dimitrakopoulos |first2=C. |last3=Jenkins |first3=K. A. |last4=Farmer |first4=D. B. |last5=Chiu |first5=H.-Y. |last6=Grill |first6=A. |last7=Avouris |first7=Ph. |title=100-GHz Transistors from Wafer-Scale Epitaxial Graphene |journal=Science |volume=327 |issue=5966 |year=2010 |pages=662–662 |issn=0036-8075 |doi=10.1126/science.1184289 |pmid=20133565|arxiv=1002.3845 |bibcode=2010Sci...327..662L }}</ref> | ||
| In June 2011, IBM researchers announced that they had succeeded in creating the first graphene-based integrated circuit, a broadband radio mixer.<ref name="LinValdes-Garcia2011">{{cite journal | |
In June 2011, IBM researchers announced that they had succeeded in creating the first graphene-based integrated circuit, a broadband radio mixer.<ref name="LinValdes-Garcia2011">{{cite journal |last=Lin |first=Y.-M. |last2=Valdes-Garcia |first2=A. |last3=Han |first3=S.-J. |last4=Farmer |first4=D. B. |last5=Meric |first5=I. |last6=Sun |first6=Y. |last7=Wu |first7=Y. |last8=Dimitrakopoulos |first8=C. |last9=Grill |first9=A. |last10=Avouris |first10=P. |last11=Jenkins |first11=K. A. |title=Wafer-Scale Graphene Integrated Circuit |journal=Science |volume=332 |issue=6035 |year=2011 |pages=1294–1297 |issn=0036-8075 |doi=10.1126/science.1204428 |pmid=21659599|bibcode=2011Sci...332.1294L }}</ref> The circuit handled frequencies up to 10 GHz. Its performance was unaffected by temperatures up to 127 C. | ||
| In June 2013 an 8 transistor 1.28 GHz ring oscillator circuit was described.<ref>{{cite web |url=http://physicsworld.com/cws/article/news/2013/jun/17/graphene-circuit-breaks-the-gigahertz-barrier |title=Graphene circuit breaks the gigahertz barrier |year=2013 }}</ref> | In June 2013 an 8 transistor 1.28 GHz ring oscillator circuit was described.<ref>{{cite web |url=http://physicsworld.com/cws/article/news/2013/jun/17/graphene-circuit-breaks-the-gigahertz-barrier |title=Graphene circuit breaks the gigahertz barrier |year=2013 }}</ref> | ||
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| ==== Transistors ==== | ==== Transistors ==== | ||
| Graphene exhibits a pronounced response to perpendicular external electric fields, potentially forming ]s (FET). A 2004 paper documented FETs with an on-off ratio of ~30 at room temperature.{{citation needed|date=May 2013}} A 2006 paper announced an all-graphene planar FET with side gates.<ref> March 14, 2006</ref> Their devices showed changes of 2% at cryogenic temperatures. The first top-gated FET (on–off ratio of <2) was demonstrated in 2007.<ref>{{Cite journal | |
Graphene exhibits a pronounced response to perpendicular external electric fields, potentially forming ]s (FET). A 2004 paper documented FETs with an on-off ratio of ~30 at room temperature.{{citation needed|date=May 2013}} A 2006 paper announced an all-graphene planar FET with side gates.<ref> March 14, 2006</ref> Their devices showed changes of 2% at cryogenic temperatures. The first top-gated FET (on–off ratio of <2) was demonstrated in 2007.<ref>{{Cite journal |last=Lemme |first=M. C. |author2=et al. |title=A graphene field-effect device |journal=IEEE Electron Device Letters |volume=28 |page=282 |year=2007 |doi=10.1109/LED.2007.891668 |arxiv=cond-mat/0703208 |bibcode=2007IEDL...28..282L |issue=4 }}</ref> Graphene nanoribbons may prove generally capable of replacing silicon as a semiconductor.<ref name="MIT1">{{Cite news |last=Bullis |first=K. |title=Graphene Transistors |publisher=] Technology Review, Inc |location=Cambridge |date=28 January 2008 |url=http://www.technologyreview.com/Nanotech/20119/ }}</ref> | ||
| | author = Bullis, K. |title = Graphene Transistors |publisher = ] Technology Review, Inc |location = Cambridge |date = 2008-01-28 |url = http://www.technologyreview.com/Nanotech/20119/ |accessdate = 2008-02-18}}</ref> | |||
| {{cite patent|US|7015142|status=patent}} for graphene-based electronics was issued in 2006. In 2008, researchers at ] produced hundreds of transistors on a single chip<ref name="Kedzierski">{{Cite journal | |
{{cite patent|US|7015142|status=patent}} for graphene-based electronics was issued in 2006. In 2008, researchers at ] produced hundreds of transistors on a single chip<ref name="Kedzierski">{{Cite journal |last=Kedzierski |first=J. |title=Epitaxial Graphene Transistors on SiC Substrates |doi=10.1109/TED.2008.926593 |journal=IEEE Transactions on Electron Devices |volume=55 |pages=2078–2085 |year=2008 |bibcode=2008ITED...55.2078K |issue=8 |last2=Hsu |first2=Pei-Lan |last3=Healey |first3=Paul |last4=Wyatt |first4=Peter W. |last5=Keast |first5=Craig L. |last6=Sprinkle |first6=Mike |last7=Berger |first7=Claire |last8=De Heer |first8=Walt A. |arxiv=0801.2744 }}</ref> and in 2009, very high frequency transistors were produced at ].<ref name="HRL">{{Cite journal |last=Moon |first=J.S. |title=Epitaxial-Graphene RF Field-Effect Transistors on Si-Face 6H-SiC Substrates |doi=10.1109/LED.2009.2020699 |journal=IEEE Electron Device Letters |volume=30 |pages=650–652 |year=2009 |bibcode=2009IEDL...30..650M |issue=6 |last2=Curtis |first2=D. |last3=Hu |first3=M. |last4=Wong |first4=D. |last5=McGuire |first5=C. |last6=Campbell |first6=P.M. |last7=Jernigan |first7=G. |last8=Tedesco |first8=J.L. |last9=Vanmil |first9=B. |last10=Myers-Ward |first10=R. |last11=Eddy |first11=C. |last12=Gaskill |first12=D.K. }}</ref> | ||
| A 2008 paper demonstrated a switching effect based on a reversible chemical modification of the graphene layer that gives an on–off ratio of greater than six orders of magnitude. These reversible switches could potentially be employed in nonvolatile memories.<ref>{{Cite journal | |
A 2008 paper demonstrated a switching effect based on a reversible chemical modification of the graphene layer that gives an on–off ratio of greater than six orders of magnitude. These reversible switches could potentially be employed in nonvolatile memories.<ref>{{Cite journal |last=Echtermeyer |first=Tim. J. |author2=et al. |journal=IEEE Electron Device Letters |volume=29 |page=952 |year=2008 |doi=10.1109/LED.2008.2001179 |title=Nonvolatile Switching in Graphene Field-Effect Devices |bibcode=2008IEDL...29..952E |issue=8 |arxiv=0805.4095 }}</ref> | ||
| In 2009, researchers demonstrated four different types of ], each composed of a single graphene transistor.<ref>{{Cite journal | |
In 2009, researchers demonstrated four different types of ], each composed of a single graphene transistor.<ref>{{Cite journal |last=Sordan |first=R. |last2=Traversi |first2=F. |last3=Russo |first3=V. |journal=Appl. Phys. Lett. |volume=94 |page=073305 |year=2009 |doi=10.1063/1.3079663 |title=Logic gates with a single graphene transistor |bibcode=2009ApPhL..94g3305S |issue=7 }}</ref> | ||
| Practical uses for these circuits are limited by the very small ] they exhibit. Typically, the amplitude of the output signal is about 40 times less than that of the input signal. Moreover, none of these circuits operated at frequencies higher than 25 kHz. | Practical uses for these circuits are limited by the very small ] they exhibit. Typically, the amplitude of the output signal is about 40 times less than that of the input signal. Moreover, none of these circuits operated at frequencies higher than 25 kHz. | ||
| In the same year, tight-binding numerical simulations<ref name |
In the same year, tight-binding numerical simulations<ref name="fiori2">Fiori G., Iannaccone G., "On the possibility of tunable-gap bilayer graphene FET", IEEE Electr. Dev. Lett., 30, 261 (2009)</ref> demonstrated that the band-gap induced in graphene bilayer field effect transistors is not sufficiently large for high-performance transistors for digital applications, but can be sufficient for ultra-low voltage applications, when exploiting a tunnel-FET architecture.<ref name="fiori3">Fiori G., Iannaccone G., "Ultralow-Voltage Bilayer graphene tunnel FET", IEEE Electr. Dev. Lett., 30, 1096 (2009)</ref> | ||
| In February 2010, researchers announced transistors with an on/off rate of 100 gigahertz, far exceeding the rates of previous attempts, and exceeding the speed of silicon transistors with an equal gate length. The {{val|240|u=nm}} devices were made with conventional silicon-manufacturing equipment.<ref name=Bourzac2010>{{Cite news | In February 2010, researchers announced transistors with an on/off rate of 100 gigahertz, far exceeding the rates of previous attempts, and exceeding the speed of silicon transistors with an equal gate length. The {{val|240|u=nm}} devices were made with conventional silicon-manufacturing equipment.<ref name=Bourzac2010>{{Cite news | ||
| | |
|last=Bourzac |first=Katherine |title=Graphene Transistors that Can Work at Blistering Speeds |work=MIT Technology Review |date=5 February 2010 |url=http://www.technologyreview.com/computing/24482/?a=f }}</ref><ref name=TW2010>. News.techworld.com. Retrieved on 2010-12-10.</ref><ref>{{Cite journal |journal=Science |title=100-GHz Transistors from Wafer-Scale Epitaxial Graphene |first7=P |last7=Avouris |first6=A |last6=Grill |first5=HY |last5=Chiu |first4=DB |last4=Farmer |first3=KA |last3=Jenkins |first2=C |last2=Dimitrakopoulos |author=Lin <!-- check this -->|volume=327 |issue=5966 |year=2010 |page=662 |pmid=20133565 |publisher=Science |doi=10.1126/science.1184289 |bibcode=2010Sci...327..662L |arxiv=1002.3845 }}</ref> | ||
| In November 2011, researchers used 3d printing (]) as a method for fabricating graphene devices.<ref>. Cornell University Library. Retrieved on 2011-29-11.</ref> | In November 2011, researchers used 3d printing (]) as a method for fabricating graphene devices.<ref>. Cornell University Library. Retrieved on 2011-29-11.</ref> | ||
| In 2013, researchers demonstrated graphene's high mobility in a detector that allows broad band frequency selectivity ranging from the THz to IR region (0.76-33THz)<ref>{{cite journal |last=Kawano |first=Yukio |title=Wide-band frequency-tunable terahertz and infrared detection with graphene |journal=Nanotechnology |year=2013 |volume=24 |issue=21 |doi=10.1088/0957-4484/24/21/214004|page=214004 |pmid=23618878|bibcode |
In 2013, researchers demonstrated graphene's high mobility in a detector that allows broad band frequency selectivity ranging from the THz to IR region (0.76-33THz)<ref>{{cite journal |last=Kawano |first=Yukio |title=Wide-band frequency-tunable terahertz and infrared detection with graphene |journal=Nanotechnology |year=2013 |volume=24 |issue=21 |doi=10.1088/0957-4484/24/21/214004|page=214004 |pmid=23618878 |bibcode=2013Nanot..24u4004K }}</ref> A separate group created a terahertz-speed transistor with bistable characteristics, which means that the device can spontaneously switch between two electronic states. The device consists of two layers of graphene separated by an insulating layer of ] a few atomic layers thick. Electrons move through this barrier by ]. These new transistors exhibit “negative differential conductance,” whereby the same electrical current flows at two different applied voltages.<ref>{{cite journal |url=http://www.kurzweilai.net/radical-new-graphene-design-operates-at-terahertz-speed |title=Radical new graphene design operates at terahertz speed |doi=10.1038/ncomms2817 |publisher=KurzweilAI |date= |accessdate=2013-05-02|arxiv=1303.6864 |bibcode=2013NatCo...4E1794B |last=Britnell |first=L. |last2=Gorbachev |first2=R. V. |last3=Geim |first3=A. K. |last4=Ponomarenko |first4=L. A. |last5=Mishchenko |first5=A. |last6=Greenaway |first6=M. T. |last7=Fromhold |first7=T. M. |last8=Novoselov |first8=K. S. |last9=Eaves |first9=L. |journal=Nature Communications |volume=4 |pages=1794– |pmid=23653206 |pmc=3644101 |issue=4 |year=2013|display-authors=9 }}<br/>{{cite DOI|10.1038/ncomms2817 }}</ref> | ||
| Graphene does not have an energy band-gap, which presents a hurdle for its applications in digital logic gates. The efforts to induce a band-gap in graphene via quantum confinement or surface functionalization have not resulted in a breakthrough. The negative differential resistance experimentally observed in graphene field-effect transistors of "conventional" design allows for construction of viable non-Boolean computational architectures with the gap-less graphene. The negative differential resistance — observed under certain biasing schemes — is an intrinsic property of graphene resulting from its symmetric band structure. The results present a conceptual change in graphene research and indicate an alternative route for graphene's applications in information processing.<ref>{{cite journal| |
Graphene does not have an energy band-gap, which presents a hurdle for its applications in digital logic gates. The efforts to induce a band-gap in graphene via quantum confinement or surface functionalization have not resulted in a breakthrough. The negative differential resistance experimentally observed in graphene field-effect transistors of "conventional" design allows for construction of viable non-Boolean computational architectures with the gap-less graphene. The negative differential resistance — observed under certain biasing schemes — is an intrinsic property of graphene resulting from its symmetric band structure. The results present a conceptual change in graphene research and indicate an alternative route for graphene's applications in information processing.<ref>{{cite journal |first=Guanxiong |last=Liu |first2=Sonia |last2=Ahsan |last3=Khitun |first3=Alexander G. |last4=Lake |first4=Roger K. |last5=Balandin |first5=Alexander A. |title=Graphene-Based Non-Boolean Logic Circuits |year=2013 |volume=114 |issue=10 |journal=Journal of Applied Physics |arxiv=1308.2931 |bibcode=2013JAP...114o4310L |page=4310 |doi=10.1063/1.4824828 }}</ref> | ||
| In 2013 researchers reported the creation of transistors printed on flexible plastic that operate at 25-gigahertz, sufficient for communications circuits and that can be fabricated at scale. The researchers first fabricate the non-graphene-containing structures—the electrodes and gates—on plastic sheets. Separately, they grow large graphene sheets on metal, then peel it off and transfer it to the plastic. Finally, they top the sheet with a waterproof layer. The devices work after being soaked in water, and are flexible enough to be folded.<ref>{{cite web |last=Bourzac |first=Katherine |url=http://www.technologyreview.com/news/518606/printed-graphene-transistors-promise-a-flexible-electronic-future/ |title=Superfast, Bendable Electronic Switches Made from Graphene | MIT Technology Review |publisher=Technologyreview.com |date= |accessdate=2013-08-24}}</ref> | In 2013 researchers reported the creation of transistors printed on flexible plastic that operate at 25-gigahertz, sufficient for communications circuits and that can be fabricated at scale. The researchers first fabricate the non-graphene-containing structures—the electrodes and gates—on plastic sheets. Separately, they grow large graphene sheets on metal, then peel it off and transfer it to the plastic. Finally, they top the sheet with a waterproof layer. The devices work after being soaked in water, and are flexible enough to be folded.<ref>{{cite web |last=Bourzac |first=Katherine |url=http://www.technologyreview.com/news/518606/printed-graphene-transistors-promise-a-flexible-electronic-future/ |title=Superfast, Bendable Electronic Switches Made from Graphene | MIT Technology Review |publisher=Technologyreview.com |date= |accessdate=2013-08-24 }}</ref> | ||
| === Redox === | === Redox === | ||
| ] can be reversibly reduced and oxidized using electrical stimulus. Controlled reduction and oxidation in two-terminal devices containing multilayer graphene oxide films are shown to result in switching between partially reduced graphene oxide and graphene, a process that modifies the electronic and optical properties. Oxidation and reduction are related to resistive switching.<ref>{{Cite journal | |
] can be reversibly reduced and oxidized using electrical stimulus. Controlled reduction and oxidation in two-terminal devices containing multilayer graphene oxide films are shown to result in switching between partially reduced graphene oxide and graphene, a process that modifies the electronic and optical properties. Oxidation and reduction are related to resistive switching.<ref>{{Cite journal |last=Ekiz |first=O.O. |author2=et al. |title=Reversible Electrical Reduction and Oxidation of Graphene Oxide |journal=ACS Nano |year=2011 |doi=10.1021/nn1014215 |volume=5 |issue=4 |pages=2475–2482 |pmid=21391707}}<br/>{{Cite journal |last=Ekiz |first=O.O. |author2=et al. |title=Supporting information for Reversible Electrical Reduction and Oxidation of Graphene Oxide |journal=ACS Nano |year=2011 |doi=10.1021/nn1014215 |volume=5 |issue=4 |pages=2475–2482 |pmid=21391707 }}</ref> | ||
| === Transparent conducting electrodes === | === Transparent conducting electrodes === | ||
| Graphene's high electrical conductivity and high optical transparency make it a candidate for transparent conducting electrodes, required for such applications as ]s, ]s, ], and ]s. In particular, graphene's mechanical strength and flexibility are advantageous compared to ], which is brittle. Graphene films may be deposited from solution over large areas.<ref name="MPI">{{Cite journal | Graphene's high electrical conductivity and high optical transparency make it a candidate for transparent conducting electrodes, required for such applications as ]s, ]s, ], and ]s. In particular, graphene's mechanical strength and flexibility are advantageous compared to ], which is brittle. Graphene films may be deposited from solution over large areas.<ref name="MPI">{{Cite journal |last=Wang |first=X. |author2=et al. |year=2007 |title=Transparent, Conductive Graphene Electrodes for Dye-Sensitized Solar Cells |journal=Nano Letters |doi=10.1021/nl072838r |volume=8 |pmid=18069877 |issue=1 |bibcode=2008NanoL...8..323W |pages=323–7 }}</ref><ref name="Eda">{{Cite journal |last=Eda |first=G |last2=Fanchini |first2=G |last3=Chhowalla |first3=M |title=Large-area ultrathin films of reduced graphene oxide as a transparent and flexible electronic material |journal=Nat Nanotechnol |volume=3 |issue=5 |pages=270–4 |year=2008 |pmid=18654522 |doi=10.1038/nnano.2008.83 }}</ref> | ||
| | last = Wang | |||
| | first = X. | |||
| | coauthors = et al. | |||
| | year = 2007 | |||
| | title = Transparent, Conductive Graphene Electrodes for Dye-Sensitized Solar Cells | |||
| | journal = Nano Letters | |||
| | doi = 10.1021/nl072838r | |||
| | volume = 8 | |||
| | pmid = 18069877 | |||
| | issue = 1 |bibcode = 2008NanoL...8..323W | |||
| | pages = 323–7 }}</ref><ref name="Eda">{{Cite journal |author=Eda G, Fanchini G, Chhowalla M |title=Large-area ultrathin films of reduced graphene oxide as a transparent and flexible electronic material |journal=Nat Nanotechnol |volume=3 |issue=5 |pages=270–4 |year=2008 |pmid=18654522 |doi=10.1038/nnano.2008.83}}</ref> | |||
| Large-area, continuous, transparent and highly conducting few-layered graphene films were produced by chemical vapor deposition and used as ]s for application in ] devices. A power conversion efficiency (PCE) up to 1.71% was demonstrated, which is 55.2% of the PCE of a control device based on indium tin oxide.<ref>{{Cite journal |title=Large area, continuous, few-layered graphene as anodes in organic photovoltaic devices |journal=Applied Physics Letters |volume=95 |page=063302 |year=2009 |doi=10.1063/1.3204698 | |
Large-area, continuous, transparent and highly conducting few-layered graphene films were produced by chemical vapor deposition and used as ]s for application in ] devices. A power conversion efficiency (PCE) up to 1.71% was demonstrated, which is 55.2% of the PCE of a control device based on indium tin oxide.<ref>{{Cite journal |title=Large area, continuous, few-layered graphene as anodes in organic photovoltaic devices |journal=Applied Physics Letters |volume=95 |page=063302 |year=2009 |doi=10.1063/1.3204698 |last=Wang |first=Yu |last2=Chen |first2=Xiaohong |last3=Zhong |first3=Yulin |last4=Zhu |first4=Furong |last5=Loh |first5=Kian Ping |bibcode=2009ApPhL..95f3302W |issue=6 }}</ref> | ||
| ]s (OLEDs) with graphene anodes have been demonstrated.<ref>{{Cite journal | ]s (OLEDs) with graphene anodes have been demonstrated.<ref>{{Cite journal |last=Wu |first=J.B. |author2=et al. |year=2010 |title=Organic Light-Emitting Diodes on Solution-Processed Graphene Transparent Electrodes |journal=ACS Nano |volume=4 |page=43 |doi=10.1021/nn900728d }}</ref> The electronic and optical performance of graphene-based devices are similar to devices made with indium tin oxide. | ||
| | last = Wu | |||
| | first = J.B. | |||
| | coauthors = et al. | |||
| | year = 2010 | |||
| | title = Organic Light-Emitting Diodes on Solution-Processed Graphene Transparent Electrodes | |||
| | journal = ACS Nano | |||
| | volume = 4 | |||
| | page = 43 | |||
| | doi= 10.1021/nn900728d | |||
| }}</ref> The electronic and optical performance of graphene-based devices are similar to devices made with indium tin oxide. | |||
| A carbon-based device called a ] (LEC) was demonstrated with chemically-derived graphene as the ] and the ] ] as the anode.<ref>{{Cite journal | A carbon-based device called a ] (LEC) was demonstrated with chemically-derived graphene as the ] and the ] ] as the anode.<ref>{{Cite journal |last=Matyba |first=P. |author2=et al. |year=2010 |title=Graphene and Mobile Ions: The Key to All-Plastic, Solution-Processed Light-Emitting Devices |journal=ACS Nano |volume=4 |doi=10.1021/nn9018569 |pmid=20131906 |issue=2 |pages=637–42 }}</ref> Unlike its predecessors, this device contains only carbon-based electrodes, with no metal. | ||
| | last = Matyba | |||
| | first = P. | |||
| | coauthors = et al. | |||
| | year = 2010 | |||
| | title = Graphene and Mobile Ions: The Key to All-Plastic, Solution-Processed Light-Emitting Devices | |||
| | journal = ACS Nano | |||
| | volume = 4 | |||
| | doi = 10.1021/nn9018569 | |||
| | pmid=20131906 | |||
| | issue = 2 | |||
| | pages = 637–42 | |||
| }}</ref> Unlike its predecessors, this device contains only carbon-based electrodes, with no metal. | |||
| === Ethanol distillation === | === Ethanol distillation === | ||
| Graphene oxide membranes allow water vapor to pass through, but are impermeable to other liquids and gases.<ref name="pmid22282806">{{cite journal |title=Unimpeded permeation of water through helium-leak-tight graphene-based membranes |doi=10.1126/science.1211694 |year=2012 |journal=Science |volume=335 |issue=6067 |pages=442–4 |pmid=22282806 |arxiv=1112.3488 | |
Graphene oxide membranes allow water vapor to pass through, but are impermeable to other liquids and gases.<ref name="pmid22282806">{{cite journal |title=Unimpeded permeation of water through helium-leak-tight graphene-based membranes |doi=10.1126/science.1211694 |year=2012 |journal=Science |volume=335 |issue=6067 |pages=442–4 |pmid=22282806 |arxiv=1112.3488 |last=Nair |first=R. R. |last2=Wu |first2=H. A. |last3=Jayaram |first3=P. N. |last4=Grigorieva |first4=I. V. |last5=Geim |first5=A. K. |bibcode=2012Sci...335..442N }}</ref> This phenomenon has been used for further distilling of ] to higher alcohol concentrations, in a room-temperature laboratory, without the application of heat or vacuum as used in traditional ] methods.<ref>{{cite news |url=http://www.dailymail.co.uk/sciencetech/article-2092321/Hi-tech-wonder-material-graphene-unexpected-use--distill-vodka-room-temperature.html |location=London |work=Daily Mail |first=Rob |last=Waugh |title=Hi-tech 'wonder material' graphene has an unexpected use – it can distill vodka at room temperature }}</ref> Further development and commercialization of such membranes could revolutionize the economics of ] production and the ] industry. | ||
| === Desalination === | === Desalination === | ||
| Research suggests that graphene filters could outperform other techniques of ] by a significant margin.<ref name="Cohen-TanugiGrossman2012">{{cite journal | |
Research suggests that graphene filters could outperform other techniques of ] by a significant margin.<ref name="Cohen-TanugiGrossman2012">{{cite journal |last=Cohen-Tanugi |first=David |last2=Grossman |first2=Jeffrey C. |title=Water Desalination across Nanoporous Graphene |journal=Nano Letters |volume=12 |issue=7 |year=2012 |pages=3602–3608 |issn=1530-6984 |doi=10.1021/nl3012853 |pmid=22668008 |bibcode=2012NanoL..12.3602C }}</ref> | ||
| === Solar cells === | === Solar cells === | ||
| Graphene has a unique combination of high electrical conductivity and optical transparency, which make it a candidate for use in solar cells. A single sheet of graphene is a zero-bandgap semiconductor whose charge carriers are delocalized over large areas, implying that carrier scattering does not occur. Because this material only absorbs 2.3% of visible light, it is a candidate for applications requiring a transparent conductor. Graphene can be assembled into a film electrode with low roughness. However, graphene films produced via solution processing contain lattice defects and grain boundaries that act as recombination centers and decrease the material's electrical conductivity. Thus, these films must be made thicker than one atomic layer to obtain useful sheet resistances. This added resistance can be combatted by incorporating conductive filler materials, such as a ] matrix. Reduced graphene film's electrical conductivity can be improved by attaching large ] such as ]-1-sulfonic acid sodium salt (PyS) and the disodium salt of 3,4,9,10-perylenetetracarboxylic diimide bisbenzenesulfonic acid (PDI). These molecules, under high temperatures, facilitate better π-conjugation of the graphene basal plane. Graphene films have high transparency in the visible and near-] regions and are chemically and thermally stable.<ref name="Mukhopadhyay 2013 202-213">{{cite book |last=Mukhopadhyay|first=Prithu |title=Graphite, Graphene and their Polymer Nanocomposites |year=2013 |publisher=Taylor & Francis Group |location=Boca Raton, Florida |isbn=978-1-4398-2779-6 |pages=202–213}}</ref> | Graphene has a unique combination of high electrical conductivity and optical transparency, which make it a candidate for use in solar cells. A single sheet of graphene is a zero-bandgap semiconductor whose charge carriers are delocalized over large areas, implying that carrier scattering does not occur. Because this material only absorbs 2.3% of visible light, it is a candidate for applications requiring a transparent conductor. Graphene can be assembled into a film electrode with low roughness. However, graphene films produced via solution processing contain lattice defects and grain boundaries that act as recombination centers and decrease the material's electrical conductivity. Thus, these films must be made thicker than one atomic layer to obtain useful sheet resistances. This added resistance can be combatted by incorporating conductive filler materials, such as a ] matrix. Reduced graphene film's electrical conductivity can be improved by attaching large ] such as ]-1-sulfonic acid sodium salt (PyS) and the disodium salt of 3,4,9,10-perylenetetracarboxylic diimide bisbenzenesulfonic acid (PDI). These molecules, under high temperatures, facilitate better π-conjugation of the graphene basal plane. Graphene films have high transparency in the visible and near-] regions and are chemically and thermally stable.<ref name="Mukhopadhyay 2013 202-213">{{cite book |last=Mukhopadhyay|first=Prithu |title=Graphite, Graphene and their Polymer Nanocomposites |year=2013 |publisher=Taylor & Francis Group |location=Boca Raton, Florida |isbn=978-1-4398-2779-6 |pages=202–213 }}</ref> | ||
| For graphene to be used in commercial solar cells, large-scale production are required. However, no scalable process for producing graphene is available, including the peeling of pyrolytic graphene or thermal decomposition of silicon carbide.<ref name="Mukhopadhyay 2013 202-213"/> | For graphene to be used in commercial solar cells, large-scale production are required. However, no scalable process for producing graphene is available, including the peeling of pyrolytic graphene or thermal decomposition of silicon carbide.<ref name="Mukhopadhyay 2013 202-213"/> | ||
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| Graphene's high charge mobilities recommend it for use as a charge collector and transporter in ]s (PV). Using graphene as a photoactive material requires its bandgap to be 1.4-1.9eV. In 2010, single cell efficiencies of nanostructured graphene-based PVs of over 12% were achieved. According to P. Mukhopadhyay and R. K. Gupta ] could be "devices in which semiconducting graphene is used as the photoactive material and metallic graphene is used as the conductive electrodes".<ref name="Mukhopadhyay 2013 202-213"/> | Graphene's high charge mobilities recommend it for use as a charge collector and transporter in ]s (PV). Using graphene as a photoactive material requires its bandgap to be 1.4-1.9eV. In 2010, single cell efficiencies of nanostructured graphene-based PVs of over 12% were achieved. According to P. Mukhopadhyay and R. K. Gupta ] could be "devices in which semiconducting graphene is used as the photoactive material and metallic graphene is used as the conductive electrodes".<ref name="Mukhopadhyay 2013 202-213"/> | ||
| In 2010，Xinming Li and Hongwei Zhu from Tsinghua University first reported graphene-silicon heterojunction solar cell,where graphene served as a transparent electrode and introduced a built-in electric field near the interface between the graphene and n-type silicon to help collect photo-generated carriers.More studies promote this new type of photovoltaic device.<ref>{{cite web|doi=10.1002/adma.200904383/abstract |title=Graphene-On-Silicon Schottky Junction Solar Cells |date= |
In 2010，Xinming Li and Hongwei Zhu from Tsinghua University first reported graphene-silicon heterojunction solar cell,where graphene served as a transparent electrode and introduced a built-in electric field near the interface between the graphene and n-type silicon to help collect photo-generated carriers.More studies promote this new type of photovoltaic device.<ref>{{cite web|doi=10.1002/adma.200904383/abstract |title=Graphene-On-Silicon Schottky Junction Solar Cells |date=9 April 2010 |doi_brokendate=2014-03-24 }}</ref> For example，in 2012 researchers from the University of Florida reported efficiency of 8.6% for a prototype cell consisting of a wafer of silicon coated with a layer of graphene doped with trifluoromethanesulfonyl-amide (TFSA). Furthermore,Xinming Li found chemical doping could improve the graphene characteristics and significantly enhance the efficiency of graphene-silicon solar cell to 9.6% in 2013.<ref>{{cite web|doi=10.1002/aenm.201300052/abstract |title=Anomalous Behaviors of Graphene Transparent Conductors in Graphene–Silicon Heterojunction Solar Cells |date=19 April 2013 |doi_brokendate=2014-03-24 }}</ref><ref>{{cite web|url=http://pubs.rsc.org/en/Content/ArticleLanding/2013/NR/c2nr33795a#!divAbstract |title=Ion doping of graphene for high-efficiency heterojunction solar cells |date=3 January 2013 }}</ref> | ||
| In 2013 another team claimed to have reached 15.6% percent using a combination of ]e and graphene as a charge collector and ] as a sunlight absorber. The device is manufacturable at temperatures under {{convert|150|C|F}} using solution-based deposition. This lowers production costs and offers the potential using flexible plastics.<ref>{{cite web|url=http://www.gizmag.com/graphene-solar-cell-record-efficiency/30466 |title=Graphene-based solar cell hits record 15.6 percent efficiency |publisher=Gizmag.com |date= |accessdate=2014-01-23}}</ref><ref>{{cite doi|10.1021/nl403997a}}</ref> | In 2013 another team claimed to have reached 15.6% percent using a combination of ]e and graphene as a charge collector and ] as a sunlight absorber. The device is manufacturable at temperatures under {{convert|150|C|F}} using solution-based deposition. This lowers production costs and offers the potential using flexible plastics.<ref>{{cite web|url=http://www.gizmag.com/graphene-solar-cell-record-efficiency/30466 |title=Graphene-based solar cell hits record 15.6 percent efficiency |publisher=Gizmag.com |date= |accessdate=2014-01-23 }}</ref><ref>{{cite doi|10.1021/nl403997a }}</ref> | ||
| Large scale production of highly transparent graphene films by ] was achieved in 2008. In this process, ultra-thin graphene sheets are created by first depositing carbon atoms in the form of graphene films on a nickel plate from ] gas. A protective layer of ] is laid over the graphene layer and the nickel underneath is dissolved in an acid bath. The final step is to attach the plastic-protected graphene to a flexible ] sheet, which can then be incorporated into an OPV cell. Graphene/polymer sheets range in size up to 150 square centimeters and can be used to create dense arrays of flexible OPV cells. It may eventually be possible to run printing presses covering extensive areas with inexpensive solar cells, much like newspaper presses print newspapers (]).<ref>{{Cite news |url=http://www.sciencedaily.com/releases/2010/07/100723095430.htm |title=Graphene organic photovoltaics: Flexible material only a few atoms thick may offer cheap solar power |work=ScienceDaily |date= |
Large scale production of highly transparent graphene films by ] was achieved in 2008. In this process, ultra-thin graphene sheets are created by first depositing carbon atoms in the form of graphene films on a nickel plate from ] gas. A protective layer of ] is laid over the graphene layer and the nickel underneath is dissolved in an acid bath. The final step is to attach the plastic-protected graphene to a flexible ] sheet, which can then be incorporated into an OPV cell. Graphene/polymer sheets range in size up to 150 square centimeters and can be used to create dense arrays of flexible OPV cells. It may eventually be possible to run printing presses covering extensive areas with inexpensive solar cells, much like newspaper presses print newspapers (]).<ref>{{Cite news |url=http://www.sciencedaily.com/releases/2010/07/100723095430.htm |title=Graphene organic photovoltaics: Flexible material only a few atoms thick may offer cheap solar power |work=ScienceDaily |date=24 July 2010}}<br/>Walker, Sohia. (2010-08-04) . Comptalks.com. Retrieved on 2010-12-10.</ref> | ||
| Silicon generates only one current-driving electron for each photon it absorbs, while graphene can produce multiple electrons. Solar cells made with graphene could offer 60% conversion efficiency – double the widely-accepted maximum efficiency of silicon cells.<ref>inhabitat.com cooperating with ICFO (Institute of Photonic Sciences)</ref> | Silicon generates only one current-driving electron for each photon it absorbs, while graphene can produce multiple electrons. Solar cells made with graphene could offer 60% conversion efficiency – double the widely-accepted maximum efficiency of silicon cells.<ref>inhabitat.com cooperating with ICFO (Institute of Photonic Sciences)</ref> | ||
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| === Single-molecule gas detection === | === Single-molecule gas detection === | ||
| Theoretically graphene makes an excellent sensor due to its 2D structure. The fact that its entire volume is exposed to its surrounding makes it very efficient to detect ] molecules. However, similar to carbon nanotubes, graphene has no dangling bonds on its surface. Gaseous molecules cannot be readily adsorbed onto graphene surfaces, so intrinsically graphene is insensitive.<ref>{{cite journal |last=Dan |first=Yaping |title=Intrinsic Response of Graphene Vapor Sensors |journal=Nano Letters |date=April 2009 |
Theoretically graphene makes an excellent sensor due to its 2D structure. The fact that its entire volume is exposed to its surrounding makes it very efficient to detect ] molecules. However, similar to carbon nanotubes, graphene has no dangling bonds on its surface. Gaseous molecules cannot be readily adsorbed onto graphene surfaces, so intrinsically graphene is insensitive.<ref>{{cite journal |last=Dan |first=Yaping |title=Intrinsic Response of Graphene Vapor Sensors |journal=Nano Letters |date=April 2009 |volume=9 |issue=4 |pages=1472–1475 |doi=10.1021/nl8033637 |last2=Lu |first2=Ye |last3=Kybert |first3=Nicholas J. |last4=Luo |first4=Zhengtang |last5=Johnson |first5=A. T. Charlie |pmid=19267449 |arxiv=0811.3091 |bibcode=2009NanoL...9.1472D }}</ref> The sensitivity of graphene chemical gas sensors can be dramatically enhanced by functionalization, for example, coating the film with a thin layer of certain polymers. The thin polymer layer acts like a concentrator that absorbs gaseous molecules. The molecule absorption introduces a local change in ] of graphene sensors. While this effect occurs in other materials, graphene is superior due to its high electrical conductivity (even when few carriers are present) and low noise, which makes this change in resistance detectable.<ref name=ChemDoping/> | ||
| === Quantum dots === | === Quantum dots === | ||
| Graphene ]s (GQDs) keep all dimensions less than 10 nm. Their size and edge ] govern their electrical, magnetic, optical and chemical properties. GQDs can be produced via graphite nanotomy<ref name |
Graphene ]s (GQDs) keep all dimensions less than 10 nm. Their size and edge ] govern their electrical, magnetic, optical and chemical properties. GQDs can be produced via graphite nanotomy<ref name="GQD">{{Cite journal |first=Nihar |last=Mohanty |first2=David |last2=Moore |first3=Zhiping |last3=Xu |first4=T. S. |last4=Sreeprasad |first5=Ashvin |last5=Nagaraja |first6=Alfredo A. |last6=Rodriguez |first7=Vikas |last7=Berry |title=Nanotomy Based Production of Transferrable and Dispersible Graphene-Nanostructures of Controlled Shape and Size |doi=10.1038/ncomms1834 |journal=Nature Communications |volume=3 |page=844 |year=2012 |issue=5 |bibcode=2012NatCo...3E.844M }}</ref> or via bottom-up, solution-based routes (]).<ref name="GQD1">{{Cite journal |last=Jinming |first=Cai |title=Atomically precise bottom-up fabrication of graphene nanoribbons |doi=10.1038/nature09211 |journal=Nature |volume=466 |page=470 |year=2010 |issue=7305|bibcode=2010Natur.466..470C |first2=Pascal |last2=Ruffieux |first=Rached |last3=Jaafar |first=Marco |last4=Bieri |first=Thomas |last5=Braun |first=Stephan |last6=Blankenburg |first=Matthias |last7=Muoth |first=Ari P. |last8=Seitsonen |first=Moussa |last9=Saleh |first=Xinliang |last10=Feng |first=Klaus |last11=Müllen |first=Roman |last12=Fasel }}</ref> GQDs with controlled structure can be incorporated into applications in electronics, optoelectronics and electromagnetics. ] can be created by changing the width of graphene nanoribbons (GNRs) at selected points along the ribbon.<ref name="Ponomarenko_2008_356">{{Cite journal |laysummary=http://news.bbc.co.uk/2/hi/technology/7352464.stm |last=Ponomarenko |first=L. A. |title=Chaotic Dirac Billiard in Graphene Quantum Dots |journal=Science |volume=320 |year=2008 |doi=10.1126/science.1154663 |pmid=18420930 |issue=5874 |bibcode=2008Sci...320..356P |pages=356–8 |last2=Schedin |first2=F. |last3=Katsnelson |first3=M. I. |last4=Yang |first4=R. |last5=Hill |first5=E. W. |last6=Novoselov |first6=K. S. |last7=Geim |first7=A. K. |arxiv=0801.0160 }}</ref><ref>{{Cite journal |last=Wang |first=Z. F. |last2=Shi |first2=Q. W. |last3=Li |first3=Q. |last4=Wang |first4=X. |last5=Hou |first5=J. G. |last6=Zheng |first6=H. |author7=et al. |title=Z-shaped graphene nanoribbon quantum dot device |doi=10.1063/1.2761266 |journal=Applied Physics Letters |volume=91 |page=053109 |year=2007 |bibcode=2007ApPhL..91e3109W |issue=5 |arxiv=0705.0023 }}</ref> | ||
| === Frequency multiplier === | === Frequency multiplier === | ||
| In 2009, researchers built experimental graphene ]s that take an incoming signal of a certain frequency and output a signal at a multiple of that frequency.<ref>{{Cite journal |laysummary |
In 2009, researchers built experimental graphene ]s that take an incoming signal of a certain frequency and output a signal at a multiple of that frequency.<ref>{{Cite journal |laysummary=http://www.physorg.com/news156698836.html |last=Wang |first=H. |last2=Nezich |first2=D. |last3=Kong |first3=J. |last4=Palacios |first4=T. |journal=IEEE Electr. Device. L. |volume=30 |page=547 |year=2009 |doi=10.1109/LED.2009.2016443 |title=Graphene Frequency Multipliers |issue=5}}<br/>{{Cite journal |first=D. |last=Cricchio |first2=P. P. |last2=Corso |first3=E. |last3=Fiordilino |first4=G. |last4=Orlando |first5=F. |last5=Persico |journal=J. Phys. B |year=2009 |volume=42 |page=085404 |doi=10.1088/0953-4075/42/8/085404 |title=A paradigm of fullerene |issue=8 |bibcode=2009JPhB...42h5404C }}</ref> | ||
| === Optical modulator === | === Optical modulator === | ||
| When the ] of graphene is tuned, its optical absorption can be changed. In 2011, researchers reported the first graphene-based optical modulator. Operating at {{val|1.2|u=GHz}} without a temperature controller, this modulator has a broad bandwidth (from 1.3 to 1.6 μm) and small footprint (~{{val|25|u=μm<sup>2</sup>}}).<ref>{{cite journal |last=Liu |first=Ming | |
When the ] of graphene is tuned, its optical absorption can be changed. In 2011, researchers reported the first graphene-based optical modulator. Operating at {{val|1.2|u=GHz}} without a temperature controller, this modulator has a broad bandwidth (from 1.3 to 1.6 μm) and small footprint (~{{val|25|u=μm<sup>2</sup>}}).<ref>{{cite journal |last=Liu |first=Ming |last2=Yin |last3=Xiaobo |last4=Ulin-Avila |last5=Erick |last6=Geng |last7=Baisong |last8=Zentgraf |last9=Thomas |last10=Ju |last11=Long |last12=Wang |last13=Feng |last14=Zhang |last15=Xiang |title=A graphene-based broadband optical modulator |journal=Nature |date=8 May 2011 |volume=474 |issue=7349 |pages=64–67 |doi=10.1038/nature10067 |pmid=21552277 |bibcode=2011Natur.474...64L }}</ref> | ||
| === Coolant additive === | === Coolant additive === | ||
| Graphene's high thermal conductivity suggests that it could be used as an additive in coolants. Preliminary research work showed that 5% graphene by volume can enhance the thermal conductivity of a base fluid by 86%.<ref>{{cite doi|10.1016/j.physleta.2011.01.040}}</ref> Another application due to graphene's enhanced thermal conductivity was found in PCR.<ref name="doi10.1088/0957-4484/23/45/455106"/> | Graphene's high thermal conductivity suggests that it could be used as an additive in coolants. Preliminary research work showed that 5% graphene by volume can enhance the thermal conductivity of a base fluid by 86%.<ref>{{cite doi|10.1016/j.physleta.2011.01.040 }}</ref> Another application due to graphene's enhanced thermal conductivity was found in PCR.<ref name="doi10.1088/0957-4484/23/45/455106"/> | ||
| === Reference material === | === Reference material === | ||
| Graphene's properties suggest it as a ] for characterizing electroconductive and transparent materials. One layer of graphene absorbs 2.3% of white light.<ref>{{Cite journal | |
Graphene's properties suggest it as a ] for characterizing electroconductive and transparent materials. One layer of graphene absorbs 2.3% of white light.<ref>{{Cite journal |first=R. R. |last=Nair |year=2008 |title=Fine Structure Constant Defines Visual Transparency of Graphene |journal=Science |pmid=18388259 |volume=320 |issue=5881 |page=1308 |doi=10.1126/science.1156965 |bibcode=2008Sci...320.1308N |last2=Blake |first2=P. |last3=Grigorenko |first3=A. N. |last4=Novoselov |first4=K. S. |last5=Booth |first5=T. J. |last6=Stauber |first6=T. |last7=Peres |first7=N. M. R. |last8=Geim |first8=A. K. }}</ref> | ||
| This property was used to define the '']'' that combines ] and ]. This parameter was used to compare materials without the use of two independent parameters.<ref>{{Cite journal | |
This property was used to define the '']'' that combines ] and ]. This parameter was used to compare materials without the use of two independent parameters.<ref>{{Cite journal |first=S. |last=Eigler |year=2009 |title=A new parameter based on graphene for characterizing transparent, conductive materials |journal=Carbon |volume=47 |pages=2936–2939 |doi=10.1016/j.carbon.2009.06.047 |issue=12 }}</ref> | ||
| === Thermal management === | === Thermal management === | ||
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| Due to graphene's high surface area to mass ratio, one potential application is in the conductive plates of ]s.<ref name="Stoller"> | Due to graphene's high surface area to mass ratio, one potential application is in the conductive plates of ]s.<ref name="Stoller"> | ||
| {{Cite journal |last |
{{Cite journal |last=Stoller |first=Meryl D. |first2=Sungjin |last2=Park |first3=Yanwu |last3=Zhu |first4=Jinho |last4=An |first5=Rodney S. |last5=Ruoff |year=2008 |url=http://bucky-central.me.utexas.edu/RuoffsPDFs/179.pdf |format=PDF |doi=10.1021/nl802558y |title=Graphene-Based Ultracapacitors |journal=Nano Lett |volume=8 |pmid=18788793 |issue=10 |bibcode=2008NanoL...8.3498S |pages=3498–502 }}</ref> | ||
| In February 2013 researchers announced a novel technique to produce graphene ]s based on the DVD burner reduction approach.<ref>{{cite web |last=Malasarn |first=Davin |url=http://newsroom.ucla.edu/portal/ucla/ucla-researchers-develop-new-technique-243553.aspx |title=UCLA researchers develop new technique to scale up production of graphene micro-supercapacitors / UCLA Newsroom |publisher=Newsroom.ucla.edu |date= |
In February 2013 researchers announced a novel technique to produce graphene ]s based on the DVD burner reduction approach.<ref>{{cite web |last=Malasarn |first=Davin |url=http://newsroom.ucla.edu/portal/ucla/ucla-researchers-develop-new-technique-243553.aspx |title=UCLA researchers develop new technique to scale up production of graphene micro-supercapacitors / UCLA Newsroom |publisher=Newsroom.ucla.edu |date=19 February 2013 }}</ref> | ||
| ==== Electrode for Li-ion batteries ==== | ==== Electrode for Li-ion batteries ==== | ||
| Stable ] cycling has recently been demonstrated in bi- and few layer graphene films grown on ] ],<ref>{{cite doi|10.1021/am301782h}}<br/>{{cite web |url=http://jes.ecsdl.org/content/159/6/A752.abstract |title=Fabrication and Electrochemical Characterization of Single and Multi-Layer Graphene Anodes for Lithium-Ion Batteries |publisher=Jes.ecsdl.org |date= |accessdate=2013-06-24}}</ref> while single layer graphene films have been demonstrated as a protective layer against corrosion in battery components such as the battery case.<ref>{{cite doi|10.1021/ja301586m}}</ref> This creates possibilities for flexible electrodes for microscale Li-ion batteries where the anode acts as the active material as well as the current collector.<ref>{{cite web |last=Johnson |first=Dexter |url=http://spectrum.ieee.org/nanoclast/semiconductors/nanotechnology/faster-and-cheaper-process-for-graphene-in-liion-batteries |title=Faster and Cheaper Process for Graphene in Li-ion Batteries - IEEE Spectrum |publisher=Spectrum.ieee.org |date= |
Stable ] cycling has recently been demonstrated in bi- and few layer graphene films grown on ] ],<ref>{{cite doi|10.1021/am301782h}}<br/>{{cite web |url=http://jes.ecsdl.org/content/159/6/A752.abstract |title=Fabrication and Electrochemical Characterization of Single and Multi-Layer Graphene Anodes for Lithium-Ion Batteries |publisher=Jes.ecsdl.org |date= |accessdate=2013-06-24 }}</ref> while single layer graphene films have been demonstrated as a protective layer against corrosion in battery components such as the battery case.<ref>{{cite doi|10.1021/ja301586m }}</ref> This creates possibilities for flexible electrodes for microscale Li-ion batteries where the anode acts as the active material as well as the current collector.<ref>{{cite web |last=Johnson |first=Dexter |url=http://spectrum.ieee.org/nanoclast/semiconductors/nanotechnology/faster-and-cheaper-process-for-graphene-in-liion-batteries |title=Faster and Cheaper Process for Graphene in Li-ion Batteries - IEEE Spectrum |publisher=Spectrum.ieee.org |date=17 January 2013 }}</ref> | ||
| There are also ] Li-ion batteries.<ref>{{cite web|last=Johnson |first=Dexter |url=http://spectrum.ieee.org/nanoclast/semiconductors/nanotechnology/graphenesilicon-anodes-for-liion-batteries-go-commercial |title=Graphene-Silicon Anodes for Li-ion Batteries Go Commercial - IEEE Spectrum |publisher=Spectrum.ieee.org |date= |
There are also ] Li-ion batteries.<ref>{{cite web|last=Johnson |first=Dexter |url=http://spectrum.ieee.org/nanoclast/semiconductors/nanotechnology/graphenesilicon-anodes-for-liion-batteries-go-commercial |title=Graphene-Silicon Anodes for Li-ion Batteries Go Commercial - IEEE Spectrum |publisher=Spectrum.ieee.org |date=21 March 2012 }}</ref><ref>{{cite web|url=http://phys.org/news/2013-04-xgs-silicon-graphene-anode-materials-lithium-ion.html |title=XGS presents new silicon-graphene anode materials for lithium-ion batteries |publisher=Phys.org |date= |accessdate=2014-02-26 }}</ref> | ||
| === Engineered piezoelectricity === | === Engineered piezoelectricity === | ||
| ] simulations predict that depositing certain ]s on graphene can render it ] responsive to an electric field applied in the out-of-plane direction. This type of locally engineered piezoelectricity is similar in magnitude to that of bulk piezoelectric materials and makes graphene a candidate for control and sensing in nanoscale devices.<ref>{{cite web |title=Straintronics: Stanford engineers create piezoelectric graphene |url=http://news.stanford.edu/news/2012/april/straintronics-piezoelectric-graphene-040312.html |publisher=Stanford University | |
] simulations predict that depositing certain ]s on graphene can render it ] responsive to an electric field applied in the out-of-plane direction. This type of locally engineered piezoelectricity is similar in magnitude to that of bulk piezoelectric materials and makes graphene a candidate for control and sensing in nanoscale devices.<ref name="stanford_2012">{{cite web |title=Straintronics: Stanford engineers create piezoelectric graphene |url=http://news.stanford.edu/news/2012/april/straintronics-piezoelectric-graphene-040312.html |publisher=Stanford University |date=3 April 2012}}<br/>{{cite journal |last=Ong |first=M. |last=Reed |first=E.J. |title=Engineered Piezoelectricity in Graphene |journal=ACS Nano |year=2012 |doi=10.1021/nn204198g |volume=6 |issue=2 |pages=1387–94 |pmid=22196055 }}</ref> | ||
| === Biodevice === | === Biodevice === | ||
| Graphene's modifiable chemistry, large surface area, atomic thickness and molecularly gatable structure make antibody-functionalized graphene sheets excellent candidates for mammalian and microbial detection and diagnosis devices.<ref name="Berry"> | Graphene's modifiable chemistry, large surface area, atomic thickness and molecularly gatable structure make antibody-functionalized graphene sheets excellent candidates for mammalian and microbial detection and diagnosis devices.<ref name="Berry">{{Cite journal |first=Nihar |last=Mohanty |first=Vikas |last=Berry |year=2008 |doi=10.1021/nl802412n |title=Graphene-based Single-Bacterium Resolution Biodevice and DNA-Transistor – Interfacing Graphene-Derivatives with Nano and Micro Scale Biocomponents |journal=Nano Letters |volume=8 |pages=4469–76 |pmid=18983201 |bibcode=2008NanoL...8.4469M |issue=12 }}</ref> | ||
| {{Cite journal | |||
| | first = Nihar | |||
| | last = Mohanty | |||
| | coauthors = Vikas Berry | |||
| | year = 2008 | |||
| | doi=10.1021/nl802412n |title = Graphene-based Single-Bacterium Resolution Biodevice and DNA-Transistor – Interfacing Graphene-Derivatives with Nano and Micro Scale Biocomponents | |||
| | journal = Nano Letters | |||
| | volume = 8 |pages = 4469–76 |pmid = 18983201 |bibcode = 2008NanoL...8.4469M | |||
| | issue = 12 }}</ref> | |||
| ]-approximation. The unoccupied (occupied) states, colored in blue–red (yellow–green), touch each other without ] exactly at the above-mentioned six k-vectors.]] | ]-approximation. The unoccupied (occupied) states, colored in blue–red (yellow–green), touch each other without ] exactly at the above-mentioned six k-vectors.]] | ||
| The most ambitious biological application of graphene is for rapid, inexpensive electronic DNA sequencing. Integration of graphene (thickness of {{val|0.34|u=nm}}) layers as nanoelectrodes into a nanopore<ref>{{Cite journal | The most ambitious biological application of graphene is for rapid, inexpensive electronic DNA sequencing. Integration of graphene (thickness of {{val|0.34|u=nm}}) layers as nanoelectrodes into a nanopore<ref name="small_5_23">{{Cite journal | ||
| |last=Xu |first=M. S. Xu |first2=D. |last2=Fujita |first3=N. |last3=Hanagata |year=2009 |pmid=19904762 |doi=10.1002/smll.200900976 |title=Perspectives and Challenges of Emerging Single-Molecule DNA Sequencing Technologies |journal=Small |volume=5 |issue=23 |pages=2638–49 }}</ref> can solve a bottleneck for nanopore-based single-molecule DNA sequencing. | |||
| | last1 = Xu | |||
| | first = M. S. Xu | |||
| | coauthors = D. Fujita and N. Hanagata | |||
| | year = 2009 | |||
| | pmid = 19904762 | |||
| | doi=10.1002/smll.200900976 |title = Perspectives and Challenges of Emerging Single-Molecule DNA Sequencing Technologies | |||
| | journal = Small | |||
| | volume = 5 | |||
| | issue = 23 |pages =2638–49}}</ref> can solve a bottleneck for nanopore-based single-molecule DNA sequencing. | |||
| On November 20, 2013 the ] awarded $100,000 to 'to develop new elastic composite materials for condoms containing nanomaterials like graphene'.<ref>{{cite news |title=Bill Gates condom challenge 'to be met' by graphene scientists |url=http://www.bbc.co.uk/news/uk-england-manchester-25016994 | |
On November 20, 2013 the ] awarded $100,000 to 'to develop new elastic composite materials for condoms containing nanomaterials like graphene'.<ref name="bbc_25016994">{{cite news |title=Bill Gates condom challenge 'to be met' by graphene scientists |url=http://www.bbc.co.uk/news/uk-england-manchester-25016994 |work=BBC News |date=20 November 2013 }}</ref> | ||
| === Radio wave absorption === | === Radio wave absorption === | ||
| Stacked graphene layers on a quartz substrate increased the absorption of millimeter (radio) waves by 90 per cent over 125 – 165 GHz bandwidth, extensible to microwave and low-terahertz frequencies, while remaining transparent to visible light. For example, graphene could be used as a coating for buildings or windows to block radio waves. Absorption is a result of mutually coupled ]s represented by each graphene-quartz substrate. A repeated transfer-and-etch process was used to control surface resistivity.<ref>{{cite web|url=http://www.kurzweilai.net/graphene-found-to-efficiently-absorb-radio-waves |title=Graphene found to efficiently absorb radio waves |publisher=KurzweilAI |date= |accessdate=2014-02-26}}</ref><ref>{{cite doi|10.1038/srep04130}}</ref> | Stacked graphene layers on a quartz substrate increased the absorption of millimeter (radio) waves by 90 per cent over 125 – 165 GHz bandwidth, extensible to microwave and low-terahertz frequencies, while remaining transparent to visible light. For example, graphene could be used as a coating for buildings or windows to block radio waves. Absorption is a result of mutually coupled ]s represented by each graphene-quartz substrate. A repeated transfer-and-etch process was used to control surface resistivity.<ref name="kurz_radio">{{cite web |url=http://www.kurzweilai.net/graphene-found-to-efficiently-absorb-radio-waves |title=Graphene found to efficiently absorb radio waves |publisher=KurzweilAI |date= |accessdate=2014-02-26 }}</ref><ref name="doi_srep04130">{{cite doi|10.1038/srep04130 }}</ref> | ||
| == Pseudo-relativistic theory{{anchor|pseudorel|reason=linked from ]}} == | == Pseudo-relativistic theory{{anchor|pseudorel|reason=linked from ]}} == | ||
| Graphene's electrical properties can be described by a conventional ] model; in this model the energy of the electrons with wave vector '''k''' is<ref name="Semenoff" /><ref name="Wallace">{{Cite journal | |
Graphene's electrical properties can be described by a conventional ] model; in this model the energy of the electrons with wave vector '''k''' is<ref name="Semenoff" /><ref name="Wallace">{{Cite journal |last=Wallace |first=P.R. |title=The Band Theory of Graphite |doi=10.1103/PhysRev.71.622 |journal=Physical Review |volume=71 |year=1947 |page=622 |bibcode=1947PhRv...71..622W |issue=9 }}</ref> | ||
| : <math>E=\pm\sqrt{\gamma_0^2\left(1+4\cos^2{\frac{k_ya}{2}}+4\cos{\frac{k_ya}{2}} \cdot \cos{\frac{k_x\sqrt{3}a}{2}}\right)}</math> | : <math>E=\pm\sqrt{\gamma_0^2\left(1+4\cos^2{\frac{k_ya}{2}}+4\cos{\frac{k_ya}{2}} \cdot \cos{\frac{k_x\sqrt{3}a}{2}}\right)}</math> | ||
| Line 700: | Line 603: | ||
| with the nearest-neighbor hopping energy γ<sub>0</sub> ≈ {{val|2.8|u=eV}} and the ] a ≈ {{val|2.46|u=Å}}. The ] and ], respectively, correspond to the different signs in the above ]; they touch each other at six points, the "K-values". However, only two of these six points are independent, while the rest are equivalent by symmetry. In the vicinity of the K-points the energy depends ''linearly'' on the wave vector, similar to a relativistic particle. Since an elementary cell of the lattice has a basis of two atoms, the ] even has an effective ]. | with the nearest-neighbor hopping energy γ<sub>0</sub> ≈ {{val|2.8|u=eV}} and the ] a ≈ {{val|2.46|u=Å}}. The ] and ], respectively, correspond to the different signs in the above ]; they touch each other at six points, the "K-values". However, only two of these six points are independent, while the rest are equivalent by symmetry. In the vicinity of the K-points the energy depends ''linearly'' on the wave vector, similar to a relativistic particle. Since an elementary cell of the lattice has a basis of two atoms, the ] even has an effective ]. | ||
| As a consequence, at low energies, even neglecting the true spin, the electrons can be described by an equation that is formally equivalent to the massless ]. This pseudo-relativistic description is restricted to the ], i.e., to vanishing rest mass ''M''<sub>0</sub>, which leads to interesting additional features:<ref name="Semenoff"/><ref name=cabra2>{{cite journal |last=Lamas |first=C.A. | |
As a consequence, at low energies, even neglecting the true spin, the electrons can be described by an equation that is formally equivalent to the massless ]. This pseudo-relativistic description is restricted to the ], i.e., to vanishing rest mass ''M''<sub>0</sub>, which leads to interesting additional features:<ref name="Semenoff" /><ref name="cabra2">{{cite journal |last=Lamas |first=C.A. |first2=D.C. |last2=Cabra |first3=N. |last3=Grandi |title=Generalized Pomeranchuk instabilities in graphene |journal=Physical Review B |year=2009 |volume=80 |issue=7 |pages=75108 |doi=10.1103/PhysRevB.80.075108 |arxiv=0812.4406|bibcode=2009PhRvB..80g5108L }}</ref> | ||
| : <math>v_F\, \vec \sigma \cdot \nabla \psi(\mathbf{r})\,=\,E\psi(\mathbf{r}).</math> | : <math>v_F\, \vec \sigma \cdot \nabla \psi(\mathbf{r})\,=\,E\psi(\mathbf{r}).</math> | ||
| Here ''v<sub>F</sub>'' ~ {{val|e=6}} is the ] in graphene, which replaces the velocity of light in the Dirac theory; <math>\vec{\sigma}</math> is the vector of the ], <math>\psi(\mathbf{r})</math> is the two-component wave function of the electrons, and ''E'' is their energy.<ref name="Castro"/> | Here ''v<sub>F</sub>'' ~ {{val|e=6}} is the ] in graphene, which replaces the velocity of light in the Dirac theory; <math>\vec{\sigma}</math> is the vector of the ], <math>\psi(\mathbf{r})</math> is the two-component wave function of the electrons, and ''E'' is their energy.<ref name="Castro" /> | ||
| == See also == | == See also == | ||
| Line 728: | Line 631: | ||
| * {{cite journal | * {{cite journal | ||
| | |
|last=Geim |first=A. K. | ||
| | |
|last2=Novoselov |first2=K. S. | ||
| | |
|year=2007 | ||
| | |
|title=The rise of graphene | ||
| | |
|journal=] | ||
| | |
|volume=6 |issue=3 |pages=183–91 | ||
| | |
|bibcode=2007NatMa...6..183G | ||
| | |
|doi=10.1038/nmat1849 | ||
| | |
|pmid=17330084 |ref=harv | ||
| }} | }} | ||
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| * | * | ||
| * National Science Foundation, March 27, 2008 | * National Science Foundation, March 27, 2008 | ||
| * {{cite web |url=http://www.nanohub.org/resource_files/2005/12/00723/2004.10.20-l21-ece453.pdf |title=Band structure of graphene |format=PDF |accessdate=2009-08-15}} | * {{cite web |url=http://www.nanohub.org/resource_files/2005/12/00723/2004.10.20-l21-ece453.pdf |format=PDF |title=Band structure of graphene |format=PDF |accessdate=2009-08-15}} | ||
| * | * | ||
| * {{cite web |url=http://physics.aps.org/articles/v2/30 |title=Pauling's dreams for graphene | |
* {{cite web |url=http://physics.aps.org/articles/v2/30 |title=Pauling's dreams for graphene |first=Antonio H. |last=Castro Neto |date=12 May 2009}} | ||
| * {{Cite journal | |
* {{Cite journal |first=N M R |last=Peres |first2=R M |last2=Ribeiro |year=2009 |title=Focus on Graphene |journal=] |volume=11 |page=095002 |doi=10.1088/1367-2630/11/9/095002 |bibcode=2009NJPh...11i5002P |issue=9 }} | ||
| * | * | ||
| * | * | ||
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| * | * | ||
| * | * | ||
| * | * | ||
| * , 15 September 2010, BBC Radio program Discovery | * , 15 September 2010, BBC Radio program Discovery | ||
Revision as of 14:58, 27 March 2014
Not to be confused with Grapheme, Graphane, or Graphyne. | This article may be too technical for most readers to understand. Please help improve it to make it understandable to non-experts, without removing the technical details. (December 2013) (Learn how and when to remove this message) |
Graphene is a 2-dimensional, crystalline allotrope of carbon. In graphene, carbon atoms are densely packed in a regular sp-bonded atomic-scale chicken wire (hexagonal) pattern. Graphene can be described as a one-atom thick layer of graphite. It is the basic structural element of other allotropes, including graphite, charcoal, carbon nanotubes and fullerenes. It can also be considered as an indefinitely large aromatic molecule, the limiting case of the family of flat polycyclic aromatic hydrocarbons.
High-quality graphene is strong, light, nearly transparent and an excellent conductor of heat and electricity. Its interactions with other materials and with light and its inherently two-dimensional nature produce unique properties, such as the bipolar transistor effect, ballistic transport of charges and large quantum oscillations.
At the time of its isolation in 2004, researchers studying carbon nanotubes were already familiar with graphene's composition, structure and properties, which had been calculated decades earlier. The combination of familiarity, extraordinary properties, surprising ease of isolation and unexpectedly high quality of the obtained graphene enabled a rapid increase in graphene research. Andre Geim and Konstantin Novoselov at the University of Manchester won the Nobel Prize in Physics in 2010 "for groundbreaking experiments regarding the two-dimensional material graphene".
Definition
"Graphene" is a combination of graphite and the suffix -ene, named by Hanns-Peter Boehm, who described single-layer carbon foils in 1962.
The term graphene first appeared in 1987 to describe single sheets of graphite as one of the constituents of graphite intercalation compounds (GICs); conceptually a GIC is a crystalline salt of the intercalant and graphene. The term was also used in early descriptions of carbon nanotubes, as well as for epitaxial graphene and polycyclic aromatic hydrocarbons.
The IUPAC compendium of technology states: "previously, descriptions such as graphite layers, carbon layers, or carbon sheets have been used for the term graphene... it is incorrect to use for a single layer a term which includes the term graphite, which would imply a three-dimensional structure. The term graphene should be used only when the reactions, structural relations or other properties of individual layers are discussed."
Graphene can be considered an "infinite alternant" (only six-member carbon ring) polycyclic aromatic hydrocarbon (PAH). The largest known isolated PAH molecule consists of 222 atoms and is 10 benzene rings across. It has proven difficult to synthesize even slightly bigger molecules, and they still remain "a dream of many organic and polymer chemists".
A definition of "isolated or free-standing graphene" was proposed: "graphene is a single atomic plane of graphite, which – and this is essential – is sufficiently isolated from its environment to be considered free-standing." This definition is narrower than the definition given above and refers to cleaved, transferred and suspended graphene monolayers. Other forms of graphene, such as graphene grown on various metals, can become free-standing if, for example, suspended or transferred to silicon dioxide (SiO
2) or silicon carbide (after its passivation with hydrogen).
History
In 1859 Benjamin Collins Brodie was aware of the highly lamellar structure of thermally reduced graphite oxide.
The structure of graphite was solved in 1916. by the related method of powder diffraction, It was studied in detail by V. Kohlschütter and P. Haenni in 1918, who also described the properties of graphite oxide paper. Its structure was determined from single-crystal diffraction in 1924.
The theory of graphene was first explored by P. R. Wallace in 1947 as a starting point for understanding the electronic properties of 3D graphite. The emergent massless Dirac equation was first pointed out by Gordon Walter Semenoff and David P. DeVincenzo and Eugene J. Mele. Semenoff emphasized the occurrence in a magnetic field of an electronic Landau level precisely at the Dirac point. This level is responsible for the anomalous integer quantum Hall effect.
The earliest TEM images of few-layer graphite were published by G. Ruess and F. Vogt in 1948. Later, single graphene layers were also observed directly by electron microscopy. Before 2004 intercalated graphite compounds were studied under a transmission electron microscope (TEM). Researchers occasionally observed thin graphitic flakes ("few-layer graphene") and possibly even individual layers. An early, detailed study on few-layer graphite dates to 1962.
Starting in the 1970s single layers of graphite were grown epitaxially on top of other materials. This "epitaxial graphene" consists of a single-atom-thick hexagonal lattice of sp-bonded carbon atoms, as in free-standing graphene. However, there is significant charge transfer from the substrate to the epitaxial graphene, and, in some cases, hybridization between the d-orbitals of the substrate atoms and π orbitals of graphene, which significantly alters the electronic structure of epitaxial graphene.
Single layers of graphite were also observed by transmission electron microscopy within bulk materials, in particular inside soot obtained by chemical exfoliation. Efforts to make thin films of graphite by mechanical exfoliation started in 1990, but nothing thinner than 50 to 100 layers was produced before 2004.
Initial attempts to make atomically thin graphitic films employed exfoliation techniques similar to the drawing method. Multilayer samples down to 10 nm in thickness were obtained. Old papers were unearthed in which researchers tried to isolate graphene starting with intercalated compounds. These papers reported the observation of very thin graphitic fragments (possibly monolayers) by transmission electron microscopy. Neither of the earlier observations was sufficient to "spark the graphene gold rush", which awaited macroscopic samples of extracted atomic planes.
One of the very first patents pertaining to the production of graphene was filed in October, 2002 (US Pat. 7071258). Entitled, "Nano-scaled Graphene Plates", this patent detailed one of the very first large scale graphene production processes. Two years later, in 2004 Andre Geim and Kostya Novoselov at University of Manchester extracted single-atom-thick crystallites from bulk graphite. They pulled graphene layers from graphite and transferred them onto thin SiO
2 on a silicon wafer in a process called either micromechanical cleavage or the Scotch tape technique. The SiO
2 electrically isolated the graphene and weakly interacted with it, providing nearly charge-neutral graphene layers. The silicon beneath the SiO
2 could be used as a "back gate" electrode to vary the charge density in the graphene over a wide range. They may not have been the first to use this technique— US 6667100 , filed in 2002, describes how to process commercially available flexible expanded graphite to achieve a graphite thickness of 0.01 thousandth of an inch. The key to success was high-throughput visual recognition of graphene on a properly chosen substrate, which provides a small but noticeable optical contrast.
The cleavage technique led directly to the first observation of the anomalous quantum Hall effect in graphene, which provided direct evidence of graphene's theoretically predicted Berry's phase of massless Dirac fermions. The effect was reported soon after by Philip Kim and Yuanbo Zhang in 2005. These experiments started after the researchers observed colleagues who were looking for the quantum Hall effect and Dirac fermions in bulk graphite.
Even though graphene on nickel and on silicon carbide have both existed in the laboratory for decades, graphene mechanically exfoliated on SiO
2 provided the first proof of the Dirac fermion nature of electrons.
Geim and Novoselov received several awards for their pioneering research on graphene, notably the 2010 Nobel Prize in Physics.
Properties
Structure
The atomic structure of isolated, single-layer graphene was studied by transmission electron microscopy (TEM) on sheets of graphene suspended between bars of a metallic grid. Electron diffraction patterns showed the expected honeycomb lattice. Suspended graphene also showed "rippling" of the flat sheet, with amplitude of about one nanometer. These ripples may be intrinsic to the material as a result of the instability of two-dimensional crystals, or may originate from the ubiquitous dirt seen in all TEM images of graphene. Atomic resolution real-space images of isolated, single-layer graphene on SiO
2 substrates are available via scanning tunneling microscopy. Photoresist residue, which must be removed to obtain atomic-resolution images, may be the "adsorbates" observed in TEM images, and may explain the observed rippling. Rippling on SiO
2 is caused by conformation of graphene to the underlying SiO
2, and is not intrinsic.
Graphene sheets in solid form usually show evidence in diffraction for graphite's (002) layering. This is true of some single-walled nanostructures. However, unlayered graphene with only (hk0) rings has been found in the core of presolar graphite onions. TEM studies show faceting at defects in flat graphene sheets and suggest a role for two-dimensional crystallization from a melt.
Graphene can self-repair holes in its sheets, when exposed to molecules containing carbon, such as hydrocarbons. Bombarded with pure carbon atoms, the atoms perfectly align into hexagons, completely filling the holes.
Chemical
Graphene is the only form of carbon (and generally all solid materials) in which each single atom is in exposure for chemical reaction from two sides (due to the 2D structure). It is known that carbon atoms at the edge of graphene sheets have special chemical reactivity, and graphene has the highest ratio of edgy carbons (in comparison with similar materials such as carbon nanotubes). In addition, various types of defects within the sheet, which are very common, increase the chemical reactivity. The onset temperature of reaction between the basal plane of single-layer graphene and oxygen gas is below 260 °C and the graphene burns at very low temperature (e.g., 350 °C). In fact, graphene is chemically the most reactive form of carbon, owing to the lateral availability of carbon atoms. Graphene is commonly modified with oxygen- and nitrogen-containing functional groups and analyzed by infrared spectroscopy and X-ray photoelectron spectroscopy. But, determination of structures of graphene with oxygen- and nitrogen- containing functional groups is a difficult task unless the structures are well controlled.
In 2013, Stanford University physicists reported that sheets of Graphene one atom thick are a hundred times more chemically reactive than thicker sheets.
Physical
The carbon–carbon bond length in graphene is about 0.142 nanometers. Graphene sheets stack to form graphite with an interplanar spacing of 0.335 nm.
Electronic
 | This section contains close paraphrasing of a non-free copyrighted source, http://www.kurzweilai.net/new-form-of-graphene-allows-electrons-to-behave-like-photons (Copyvios report). Relevant discussion may be found on the talk page. Please help Misplaced Pages by rewriting this section with your own words. (March 2014) (Learn how and when to remove this message) |
Graphene differs from most three-dimensional materials. Intrinsic graphene is a semi-metal or zero-gap semiconductor. Understanding the electronic structure of graphene is the starting point for finding the band structure of graphite. The energy-momentum relation (dispersion relation) is linear for low energies near the six corners of the two-dimensional hexagonal Brillouin zone, leading to zero effective mass for electrons and holes. Due to this linear (or "conical") dispersion relation at low energies, electrons and holes near these six points, two of which are inequivalent, behave like relativistic particles described by the Dirac equation for spin-1/2 particles. Hence, the electrons and holes are called Dirac fermions and the six corners of the Brillouin zone are called the Dirac points. The equation describing the electrons' linear dispersion relation is ; where the Fermi velocity vF ~ 10 m/s, and the wavevector k is measured from the Dirac points (the zero of energy is chosen here to coincide with the Dirac points).
; where the Electrical resistance in 40-nanometer-wide nanoribbons of epitaxially-applied graphene changes in discrete steps following quantum mechanical principles. Graphene nanoribbons can act more like optical waveguides or quantum dots, allowing electrons to flow smoothly along the material's edges. In conductors such as copper, resistance increases in proportion to the length as electrons encounter more and more impurities while moving through the conductor. Electrons travel ballistically, similar to those observed in cylindrical carbon nanotubes, exceeding theoretical conductance predictions for graphene by a factor of 10. Electrons in the nanoribbons can move tens or hundreds of microns without scattering.
The measured graphene nanoribbons were approximately 40 nanometers wide that had been grown on the edges of three-dimensional structures etched into silicon carbide wafers. When the wafers are heated to approximately 1,000 °C (1,830 °F), silicon is preferentially driven off along the edges, forming graphene nanoribbons whose structure is determined by the pattern of the three-dimensional surface.
The nanoribbons have perfectly smooth edges, annealed by the fabrication process. Electrons on the edge flow more like photons in optical fiber, helping them avoid scattering. Ballistic conductance extended for up to 16 microns. Electron mobility measurements surpassing one million correspond to a sheet resistance of one ohm per square— two orders of magnitude lower than what is observed in two-dimensional graphene and one tenth of theoretical predictions.
Transport is dominated by two modes. One is ballistic and temperature independent; while the other is thermally activated. Transport is protected from back-scattering, possibly reflecting ground-state properties of neutral graphene. At room temperature, the resistance of both modes is found to increase abruptly at a particular length—the ballistic mode at 16 micrometres and the other at 160 nanometres.
Theoretical explanations of the phenomenon are incomplete, although they may produce a new type of electronic transport similar to what is observed in superconductors.
"Massive" electrons
Graphene's unit cell has two identical carbon atoms and two zero-energy states: one in which the electron resides on atom A, the other in which the electron resides on atom B. Both states exist at exactly zero energy. However, if the two atoms in the unit cell are not identical, the situation changes. Hunt et al. show that placing hBN in contact with graphene can alter the potential felt at atom A versus atom B enough that the electrons develop a mass and accompanying band gap of about 30 meV.
The mass can be positive or negative. An arrangement that slightly raises the energy of an electron on atom A relative to atom B gives it a positive mass, while an arrangement that raises the energy of atom B produces a negative electron mass. The two versions behave alike and are indistinguishable via optical spectroscopy. An electron traveling from a positive-mass region to a negative-mass region must cross an intermediate region where its mass once again becomes zero. This region is gapless and therefore metallic. Metallic modes bounding semiconducting regions of opposite-sign mass is a hallmark of a topological phase and display much the same physics as topological insulators.
If the mass in graphene can be controlled, electrons can be confined to massless regions by surrounding them with massive regions, allowing the patterning of quantum dots, wires, and other mesoscopic structures. It also produces one-dimensional conductors along the boundary. These wires would be protected against backscattering and could carry currents without dissipation.
Electron transport
Experimental results from transport measurements show that graphene has a remarkably high electron mobility at room temperature, with reported values in excess of 15,000 cm·V·s. Additionally, the symmetry of the experimentally measured conductance indicates that hole and electron mobilities should be nearly the same. The mobility is nearly independent of temperature between 10 K and 100 K, which implies that the dominant scattering mechanism is defect scattering. Scattering by the acoustic phonons of graphene intrinsically limits room temperature mobility to 200,000 cm·V·s at a carrier density of 10 cm. The corresponding resistivity of the graphene sheet would be 10 Ω·cm. This is less than the resistivity of silver, the lowest known at room temperature. However, for graphene on SiO
2 substrates, scattering of electrons by optical phonons of the substrate is a larger effect at room temperature than scattering by graphene’s own phonons. This limits mobility to 40,000 cm·V·s.
Despite zero carrier density near the Dirac points, graphene exhibits a minimum conductivity on the order of . The origin of this minimum conductivity is still unclear. However, rippling of the graphene sheet or ionized impurities in the SiO
2 substrate may lead to local puddles of carriers that allow conduction. Several theories suggest that the minimum conductivity should be ; however, most measurements are of order or greater and depend on impurity concentration.
. The origin of this minimum conductivity is still unclear. However, rippling of the graphene sheet or ionized impurities in the SiO
; however, most measurements are of order Graphene doped with various gaseous species (both acceptors and donors) can be returned to an undoped state by gentle heating in vacuum. Even for dopant concentrations in excess of 10 cm carrier mobility exhibits no observable change. Graphene doped with potassium in ultra-high vacuum at low temperature can reduce mobility 20-fold. The mobility reduction is reversible on heating the graphene to remove the potassium.
Due to graphene's two dimensions, charge fractionalization (where the apparent charge of individual pseudoparticles in low-dimensional systems is less than a single quantum) is thought to occur. It may therefore be a suitable material for constructing quantum computers using anyonic circuits.
Optical
Graphene's unique optical properties produce an unexpectedly high opacity for an atomic monolayer in vacuum, absorbing πα ≈ 2.3% of white light, where α is the fine-structure constant. This is a consequence of the "unusual low-energy electronic structure of monolayer graphene that features electron and hole conical bands meeting each other at the Dirac point... is qualitatively different from more common quadratic massive bands". Based on the Slonczewski–Weiss–McClure (SWMcC) band model of graphite, the interatomic distance, hopping value and frequency cancel when optical conductance is calculated using Fresnel equations in the thin-film limit.
Although confirmed experimentally, the measurement is not precise enough to improve on other techniques for determining the fine-structure constant.
Graphene's band gap can be tuned from 0 to 0.25 eV (about 5 micrometre wavelength) by applying voltage to a dual-gate bilayer graphene field-effect transistor (FET) at room temperature. The optical response of graphene nanoribbons is tunable into the terahertz regime by an applied magnetic field. Graphene/graphene oxide systems exhibit electrochromic behavior, allowing tuning of both linear and ultrafast optical properties.
A graphene-based Bragg grating (one-dimensional photonic crystal) has been fabricated and demonstrated its capability for excitation of surface electromagnetic waves in the periodic structure by using 633 nm He-Ne laser as the light source.
Saturable absorption
Such unique absorption could become saturated when the input optical intensity is above a threshold value. This nonlinear optical behavior is termed saturable absorption and the threshold value is called the saturation fluence. Graphene can be saturated readily under strong excitation over the visible to near-infrared region, due to the universal optical absorption and zero band gap. This has relevance for the mode locking of fiber lasers, where fullband mode locking has been achieved by graphene-based saturable absorber. Due to this special property, graphene has wide application in ultrafast photonics. Moreover, the optical response of graphene/graphene oxide layers can be tuned electrically. Saturable absorption in graphene could occur at the Microwave and Terahertz band, owing to its wideband optical absorption property. The microwave saturable absorption in graphene demonstrates the possibility of graphene microwave and terahertz photonics devices, such as microwave saturable absorber, modulator, polarizer, microwave signal processing and broad-band wireless access networks.
Nonlinear Kerr effect
Under more intensive laser illumination, graphene could also possess a nonlinear phase shift due to the optical nonlinear Kerr effect. Based on a typical open and close aperture z-scan measurement, graphene possesses a giant non-linear Kerr coefficient of 10 cm·W, almost nine orders of magnitude larger than that of bulk dielectrics. This suggests that graphene may be a nonlinear Kerr medium, paving the way for graphene-based nonlinear Kerr photonics such as a soliton.
Excitonic
First-principle calculations with quasiparticle corrections and many-body effects are performed to study the electronic and optical properties of graphene-based materials. The approach is described as three stages. With GW calculation, the properties of graphene-based materials are accurately investigated, including graphene, graphene nanoribbons, edge and surface functionalized armchair graphene nanoribbons, hydrogen saturated armchair graphene nanoribbons, Josephson effect in graphene SNS junctions with single localized defect and scaling properties in armchair graphene nanoribbons.
Thermal
Stability
Ab initio calculations show that a graphene sheet is thermodynamically unstable if its size is less than about 20 nm (“graphene is the least stable structure until about 6000 atoms”) and becomes the most stable fullerene (as within graphite) only for molecules larger than 24,000 atoms.
Conductivity
The near-room temperature thermal conductivity of graphene was measured to be between (4.84±0.44) × 10 to (5.30±0.48) × 10 W·m·K. These measurements, made by a non-contact optical technique, are in excess of those measured for carbon nanotubes or diamonds. The isotopic composition, the ratio of C to C, has a significant impact on thermal conductivity, where isotopically pure C graphene has higher conductivity than either a 50:50 isotope ratio or the naturally occurring 99:1 ratio. It can be shown by using the Wiedemann–Franz law, that the thermal conduction is phonon-dominated. However, for a gated graphene strip, an applied gate bias causing a Fermi energy shift much larger than kBT can cause the electronic contribution to increase and dominate over the phonon contribution at low temperatures. The ballistic thermal conductance of graphene is isotropic.
Potential for this high conductivity can be seen by considering graphite, a 3D version of graphene that has basal plane thermal conductivity of over a 1000 W·m·K (comparable to diamond). In graphite, the c-axis (out of plane) thermal conductivity is over a factor of ~100 smaller due to the weak binding forces between basal planes as well as the larger lattice spacing. In addition, the ballistic thermal conductance of graphene is shown to give the lower limit of the ballistic thermal conductances, per unit circumference, length of carbon nanotubes.
Despite its 2-D nature, graphene has 3 acoustic phonon modes. The two in-plane modes (LA, TA) have a linear dispersion relation, whereas the out of plane mode (ZA) has a quadratic dispersion relation. Due to this, the T dependent thermal conductivity contribution of the linear modes is dominated at low temperatures by the T contribution of the out of plane mode. Some graphene phonon bands display negative Grüneisen parameters. At low temperatures (where most optical modes with positive Grüneisen parameters are still not excited) the contribution from the negative Grüneisen parameters will be dominant and thermal expansion coefficient (which is directly proportional to Grüneisen parameters) negative. The lowest negative Grüneisen parameters correspond to the lowest transversal acoustic ZA modes. Phonon frequencies for such modes increase with the in-plane lattice parameter since atoms in the layer upon stretching will be less free to move in the z direction. This is similar to the behavior of a string, which, when it is stretched, will have vibrations of smaller amplitude and higher frequency. This phenomenon, named "membrane effect", was predicted by Lifshitz in 1952.
Mechanical
The flat graphene sheet is unstable with respect to scrolling i.e. bending into a cylindrical shape, which is its lower-energy state.
As of 2009, graphene appeared to be one of the strongest materials known with a breaking strength over 100 times greater than a hypothetical steel film of the same (thin) thickness, with a Young's modulus (stiffness) of 1 TPa (150,000,000 psi). The Nobel announcement illustrated this by saying that a 1 square meter graphene hammock would support a 4 kg cat but would weigh only as much as one of the cat's whiskers, at 0.77 mg (about 0.001% of the weight of 1 m of paper).
However, the process of separating it from graphite, where it occurs naturally, requires technological development to be economical enough to be used in industrial processes.
The spring constant of suspended graphene sheets has been measured using an atomic force microscope (AFM). Graphene sheets, held together by van der Waals forces, were suspended over SiO
2 cavities where an AFM tip was probed to test its mechanical properties. Its spring constant was in the range 1–5 N/m and the stiffness was 0.5 TPa, which differs from that of bulk graphite. These high values make graphene very strong and rigid. These intrinsic properties could lead to using graphene for NEMS applications such as pressure sensors and resonators.
As is true of all materials, regions of graphene are subject to thermal and quantum fluctuations in relative displacement. Although the amplitude of these fluctuations is bounded in 3D structures (even in the limit of infinite size), the Mermin-Wagner theorem shows that the amplitude of long-wavelength fluctuations grows logarithmically with the scale of a 2D structure, and would therefore be unbounded in structures of infinite size. Local deformation and elastic strain are negligibly affected by this long-range divergence in relative displacement. It is believed that a sufficiently large 2D structure, in the absence of applied lateral tension, will bend and crumple to form a fluctuating 3D structure. Researchers have observed ripples in suspended layers of graphene, and it has been proposed that the ripples are caused by thermal fluctuations in the material. As a consequence of these dynamical deformations, it is debatable whether graphene is truly a 2D structure.
Spin transport
Graphene is claimed to be an ideal material for spintronics due to its small spin-orbit interaction and the near absence of nuclear magnetic moments in carbon (as well as a weak hyperfine interaction). Electrical spin current injection and detection has been demonstrated up to room temperature. Spin coherence length above 1 micrometre at room temperature was observed, and control of the spin current polarity with an electrical gate was observed at low temperature.
Anomalous quantum Hall effect
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The quantum Hall effect is relevant for accurate measuring of electrical quantities, and in 1985 Klaus von Klitzing received the Nobel prize for its discovery. The effect concerns the dependence of a transverse conductivity on a magnetic field, which is perpendicular to a current-carrying stripe. Usually the phenomenon, the quantization of the so-called Hall conductivity at integer multiples (the "Landau level") of the basic quantity (where e is the elementary electric charge and h is Planck's constant) can be observed only in very clean silicon or gallium arsenide solids at very low temperatures around 3 K and very high magnetic fields.
at integer multiples (the "
(where e is the elementary electric charge and h is In contrast graphene shows the quantum Hall effect just in the presence of a magnetic field and just with respect to conductivity-quantization: the effect is anomalous in that the sequence of steps is shifted by 1/2 with respect to the standard sequence and with an additional factor of 4. Graphene's Hall conductivity is , where N is the Landau level and the double valley and double spin degeneracies give the factor of 4. Moreover, in graphene these anomalies are present at room temperature, i.e. at roughly 20 °C. This anomalous behavior is a direct result of graphene's massless Dirac electrons. In a magnetic field, their spectrum has a Landau level with energy precisely at the Dirac point. This level is a consequence of the Atiyah–Singer index theorem and is half-filled in neutral graphene, leading to the "+1/2" in the Hall conductivity. Bilayer graphene also shows the quantum Hall effect, but with only one of the two anomalies (i.e. ). In the second anomaly, the first plateau at N=0 is absent, indicating that bilayer graphene stays metallic at the neutrality point.
, where N is the Landau level and the double valley and double spin degeneracies give the factor of 4. Moreover, in graphene these anomalies are present at room temperature, i.e. at roughly 20 °C. This anomalous behavior is a direct result of graphene's massless Dirac electrons. In a magnetic field, their spectrum has a Landau level with energy precisely at the Dirac point. This level is a consequence of the 
). In the second anomaly, the first plateau at N=0 is absent, indicating that bilayer graphene stays metallic at the neutrality point.
Unlike normal metals, graphene's longitudinal resistance shows maxima rather than minima for integral values of the Landau filling factor in measurements of the Shubnikov–De Haas oscillations, which show a phase shift of π, known as Berry’s phase. Berry’s phase arises due to the zero effective carrier mass near the Dirac points. Study of the temperature dependence of graphene's Shubnikov–de Haas oscillations reveals that the carriers have a non-zero cyclotron mass, despite their zero effective mass from the E–k relation.
Graphene samples prepared on nickel films, and on both the silicon face and carbon face of silicon carbide, show the anomalous quantum Hall effect directly in electrical measurements. Graphitic layers on the carbon face of silicon carbide show a clear Dirac spectrum in angle-resolved photoemission experiments, and the anomalous quantum Hall effect is observed in cyclotron resonance and tunneling experiments.
Strong magnetic fields
Graphene's quantum Hall effect in magnetic fields above 10 Teslas or so reveals additional interesting features. Additional plateaus of the Hall conductivity at with are observed. Also, the observation of a plateau at and the fractional quantum Hall effect at were reported.
with 
are observed. Also, the observation of a plateau at 
and the fractional quantum Hall effect at 
were reported.
These observations with indicate that the four-fold degeneracy (two valley and two spin degrees of freedom) of the Landau energy levels is partially or completely lifted. One hypothesis is that the magnetic catalysis of symmetry breaking is responsible for lifting the degeneracy.
indicate that the four-fold degeneracy (two valley and two spin degrees of freedom) of the Landau energy levels is partially or completely lifted. One hypothesis is that the Forms
Nanostripes
Graphene nanoribbons ("nanostripes" in the "zig-zag" orientation), at low temperatures, show spin-polarized metallic edge currents, which also suggests applications in the new field of spintronics. (In the "armchair" orientation, the edges behave like semiconductors.)
Graphene oxide
Further information: Graphite oxideUsing paper-making techniques on dispersed, oxidized and chemically processed graphite in water, the monolayer flakes form a single sheet and create strong bonds. These sheets, called graphene oxide paper have a measured tensile modulus of 32 GPa. The chemical property of graphite oxide is related to the functional groups attached to graphene sheets. These can change the polymerization pathway and similar chemical processes. Graphene oxide flakes in polymers display enhanced photo-conducting properties. Graphene-based membranes are impermeable to all gases and liquids (vacuum-tight). However, water evaporates through them as quickly as if the membrane was not present.
Chemical modification
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Soluble fragments of graphene can be prepared in the laboratory through chemical modification of graphite. First, microcrystalline graphite is treated with an acidic mixture of sulfuric acid and nitric acid. A series of oxidation and exfoliation steps produce small graphene plates with carboxyl groups at their edges. These are converted to acid chloride groups by treatment with thionyl chloride; next, they are converted to the corresponding graphene amide via treatment with octadecylamine. The resulting material (circular graphene layers of 5.3 angstrom thickness) is soluble in tetrahydrofuran, tetrachloromethane and dichloroethane.
Refluxing single-layer graphene oxide (SLGO) in solvents leads to size reduction and folding of individual sheets as well as loss of carboxylic group functionality, by up to 20%, indicating thermal instabilities of SLGO sheets dependant on their preparation methodology. When using thionyl chloride, acyl chloride groups result, which can then form aliphatic and aromatic amides with a reactivity conversion of around 70–80%.
Hydrazine reflux is commonly used for reducing SLGO to SLG(R), but titrations show that only around 20–30% of the carboxylic groups are lost, leaving a significant number available for chemical attachment. Analysis of SLG(R) generated by this route reveals that the system is unstable and using a room temperature stirring with HCl (< 1.0 M) leads to around 60% loss of COOH functionality. Room temperature treatment of SLGO with carbodiimides leads to the collapse of the individual sheets into star-like clusters that exhibited poor subsequent reactivity with amines (ca. 3–5% conversion of the intermediate to the final amide). It is apparent that conventional chemical treatment of carboxylic groups on SLGO generates morphological changes of individual sheets that leads to a reduction in chemical reactivity, which may potentially limit their use in composite synthesis. Therefore, chemical reactions types have been explored. SLGO has also been grafted with polyallylamine, cross-linked through epoxy groups. When filtered into graphene oxide paper, these composites exhibit increased stiffness and strength relative to unmodified graphene oxide paper.
Full hydrogenation from both sides of graphene sheet results in graphane, but partial hydrogenation leads to hydrogenated graphene. Similarly, both-side fluorination of graphene (or chemical and mechanical exfoliation of graphite fluoride) leads to fluorographene (graphene fluoride), while partial fluorination (generally halogenation) provides fluorinated (halogenated) graphene.
Casimir effect and dispersion
The Casimir effect is an interaction between any disjoint neutral bodies provoked by the fluctuations of the electrodynamical vacuum. Mathematically it can be explained by considering the normal modes of electromagnetic fields, which explicitly depend on the boundary (or matching) conditions on the surfaces of the interacting bodies. Since the interaction of graphene with an electromagnetic field is surprisingly strong for a one-atom-thick material, the Casimir effect is of growing interest.
The related van der Waals force (or dispersion force) is also unusual, obeying an inverse cubic, asymptotic power law in contrast to the usual inverse quartic.
Bilayer graphene
Main article: Bilayer grapheneBilayer graphene displays the anomalous quantum Hall effect, a tunable band gap and potential for excitonic condensation –making them promising candidates for optoelectronic and nanoelectronic applications. Bilayer graphene typically can be found either in twisted configurations where the two layers are rotated relative to each other or graphitic Bernal stacked configurations where half the atoms in one layer lie atop half the atoms in the other. Stacking order and orientation govern the optical and electronic properties of bilayer graphene.
One way to synthesize bilayer graphene is via chemical vapor deposition, and can produce large bilayer regions that almost exclusively conform to a Bernal stack geometry.
Graphene Fiber
In 2011, Xinming Li and Hongwei Zhu from Tsinghua University reported a novel yet simple approach to fabricate graphene fibers from chemical vapor deposition grown graphene films. The method was scalable and controllable, delivering tunable morphology and pore structure by controlling the evaporation of solvents with suitable surface tension. Flexible all-solid-state supercapacitors based on this graphene fibers were demonstrated in 2013.
3D graphene
In 2013, a three-dimensional honeycomb of hexagonally arranged carbon was termed 3D graphene, although self-supporting 3D graphene has not yet been produced.
Production techniques
True isolated 2D crystals cannot be grown via chemical synthesis beyond small sizes even in principle. However, other routes to 2d materials exist:
Fundamental forces place seemingly insurmountable barriers in the way of creating ... The nascent 2D crystallites try to minimize their surface energy and inevitably morph into one of the rich variety of stable 3D structures that occur in soot. But there is a way around the problem. Interactions with 3D structures stabilize 2D crystals during growth. So one can make 2D crystals sandwiched between or placed on top of the atomic planes of a bulk crystal. In that respect, graphene already exists within graphite... One can then hope to fool Nature and extract single-atom-thick crystallites at a low enough temperature that they remain in the quenched state prescribed by the original higher-temperature 3D growth.
Graphene planes become better separated in intercalated graphite compounds.
Graphene fragments are produced (along with other debris) whenever graphite is abraded, such as when drawing with a pencil.
In 2011 the Institute of Electronic Materials Technology and Department of Physics at Warsaw University announced Sicilicon-based epitaxy technology for producing large pieces of graphene with the best quality to date.
Mechanical exfoliation
This involves splitting single layers of graphene from multi-layered graphite. Achieving single layers typically requires multiple exfoliation steps, each producing a slice with fewer layers, until only one remains. Geim and Novosolev used adhesive tape to split the layers.
After exfoliation the flakes are deposited on a silicon wafer using "dry deposition". Individual atomic planes can be viewed with an optical microscope. Crystallites larger than 1 mm and visible to the naked eye can be obtained with the technique. It is often referred to as a "scotch tape" or "drawing" method. The latter name appeared because the dry deposition resembles drawing with a piece of graphite.
Epitaxy
Epitaxy refers to the deposition of a crystalline overlayer on a crystalline substrate, where there is registry between the two. In some cases epitaxial graphene layers are coupled to surfaces weakly enough (by Van der Waals forces) to retain the two dimensional electronic band structure of isolated graphene. An example of weakly coupled epitaxial graphene is the one grown on SiC.
Graphene monolayers grown on SiC and Ir are weakly coupled to these substrates (how weakly remains debated) and the graphene–substrate interaction can be further passivated.
Silicon carbide
Main article: Carbide-derived CarbonHeating silicon carbide (SiC) to high temperatures (>1100 °C) under low pressures (~10 torr) reduces it to graphene. This process produces epitaxial graphene with dimensions dependent upon the size of the wafer. The face of the SiC used for graphene formation, silicon- or carbon-terminated, highly influences the thickness, mobility and carrier density of the resulting graphene.
The electronic band-structure (so-called Dirac cone structure) was first visualized in this material. Weak anti-localization is observed in this material, but not in exfoliated graphene produced by the pencil-trace method. Large, temperature-independent mobilities have been observed, approaching those in exfoliated graphene placed on silicon oxide, but lower than mobilities in suspended graphene produced by the drawing method. Even without transfer, graphene on SiC exhibits massless Dirac fermions.
The weak van der Waals force that provides the cohesion of multilayer graphene stacks does not always affect the electronic properties of the individual graphene layers in the stack. That is, while the electronic properties of certain multilayered epitaxial graphenes are identical to that of a single layer, in other cases the properties are affected, as they are in bulk graphite. This effect is well understood theoretically and is related to the symmetry of the interlayer interactions.
Epitaxial graphene on SiC can be patterned using standard microelectronics methods. The band gap can be tuned by laser irradiation.
Metal substrates
The atomic structure of a metal substrate can seed the growth of graphene. Graphene grown on ruthenium does not typically produce uniform layer thickness. Bonding between the bottom graphene layer and the substrate may affect layer properties.
Graphene grown on iridium is very weakly bonded, uniform in thickness and can be highly ordered. As on many other substrates, graphene on iridium is slightly rippled. Due to the long-range order of these ripples, minigaps in the electronic band-structure (Dirac cone) become visible. High-quality sheets of few-layer graphene exceeding 1 cm (0.2 sq in) in area have been synthesized via chemical vapor deposition on thin nickel films with methane as a carbon source. These sheets have been successfully transferred to various substrates.
An improvement of this technique employs copper foil; at very low pressure, the growth of graphene automatically stops after a single graphene layer forms. Arbitrarily large films can be created. The single layer growth is also due to low concentration of carbon in methane. Larger hydrocarbons such as ethane and propane produce bilayer graphene. Atmospheric pressure CVD growth produces multilayer graphene on copper (similar to that grown on nickel films). Graphene has been demonstrated at temperatures compatible with conventional CMOS processing, using a nickel-based alloy with gold as catalyst.
Reduction of graphite oxide
Graphite oxide reduction was probably the first method of graphene synthesis. P. Boehm reported producing monolayer flakes of reduced graphene oxide in 1962. Geim acknowledged Boehm's contribution. Rapid heating of graphite oxide and exfoliation yields highly dispersed carbon powder with a few percent of graphene flakes. Reduction of graphite oxide monolayer films, e.g. by hydrazine, annealing in argon/hydrogen, was reported to yield graphene films. However, the quality is lower compared to scotch-tape graphene, due to incomplete removal of functional groups. Furthermore, the oxidation protocol introduces permanent defects due to over-oxidation. Recently, the oxidation protocol was enhanced to yield graphene oxide with an almost intact carbon framework that allows highly efficient removal of functional groups. The measured charge carrier mobility exceeded 1,000 centimetres (393.70 in)/Vs. Spectroscopic analysis of reduced graphene oxide has been conducted.
Applying a layer of graphite oxide film to a DVD and burning it in a DVD writer produced a thin graphene film with high electrical conductivity (1738 siemens per meter) and specific surface area (1520 square meters per gram), and was highly resistant and malleable.
Metal-carbon melts
This process dissolves carbon atoms inside a transition metal melt at a certain temperature and then precipitates the dissolved carbon at lower temperatures as single layer graphene (SLG).
The metal is first melted in contact with a carbon source, possibly a graphite crucible inside which the melt is carried out or graphite powder or chunks that are placed in the melt. Keeping the melt in contact with the carbon at a specific temperature dissolves the carbon atoms, saturating the melt based on the binary phase diagram of metal-carbon. Upon lowering the temperature, carbon's solubility decreases and the excess carbon precipitates atop the melt. The floating layer can be either skimmed or frozen for later removal. Using different morphology, including thick graphite, few layer graphene (FLG) and SLG were observed on metal substrate. Raman spectroscopy proved that SLG had grown on nickel substrate. The SLG Raman spectrum featured no D and D′ band, indicating its pristine nature. Among transition metals, nickel provides the best substrate for growing SLG. Since nickel is not Raman active, direct Raman spectroscopy of graphene layers on top of the nickel is achievable.
Sodium ethoxide pyrolysis
Gram-quantities of graphene were produced by the reduction of ethanol by sodium metal, followed by pyrolysis of the ethoxide product and washing with water to remove sodium salts.
Nanotube slicing
Graphene can be created by cutting open carbon nanotubes. In one such method multi-walled carbon nanotubes are cut open in solution by action of potassium permanganate and sulfuric acid. In another method graphene nanoribbons were produced by plasma etching of nanotubes partly embedded in a polymer film.
Solvent exfoliation
Dispersing graphite in a proper liquid medium can produce graphene by sonication. Non-exfoliated graphite is separated from graphene by centrifugation, producing graphene concentrations initially up to 0.01 mg/ml in N-methylpyrrolidone (NMP) and later to 2.1 mg/ml in NMP,. Using a suitable ionic liquid as the dispersing liquid medium for graphite exfoliation produced concentrations of 5.33 mg/ml. The concentration of graphene sheets produced by this method is very low because there is nothing preventing the sheets from restacking due to the van der Waals forces pulling them back together. the maximum concentrations achieved are the points at which the van der Waals forces overcome the interactive forces between the graphene sheets and the solvent molecules.
Surfactant-aided exfoliation
Similar to solvent exfoliation, graphite is sonicated in a suitable solvent. In this case, however, surfactant molecules are added which prevent the restacking of the graphene sheets by adsorbing to the surface of the graphene. The concentration of graphene achieved by this method is higher than solvent exfoliation, but the removal of the surfactant molecules is often necessary and usually requires chemical treatments.
Interface trapping
Macro-scale graphene films can be created by sonicating graphite while at the interface of two immiscible liquids, most notably heptane and water. The graphene sheets are exfoliated because of the sonication and then adsorbed to the high energy interface between the heptane and the water, where they are kept from restacking. The force holding the graphene at the interface is very strong, withstanding forces in excess of 300,000 g. The solvents may then be evaporated, leaving behind the graphene film. Films created using the interface trapping method are very transparent (up to ~95 %T) and conductive.
Carbon dioxide reduction
A highly exothermic reaction combusts magnesium in an oxidation-reduction reaction with carbon dioxide, producing a variety of carbon nanoparticles including graphene and fullerenes. The carbon dioxide reactant may be either solid (dry-ice) or gaseous. The products of this reaction are carbon and magnesium oxide. US patent 8377408 was issued for this process.
Potential applications
Potential applications include lightweight, thin, flexible, yet durable display screens, electric circuits, and solar cells, as well as various medical, chemical and industrial processes enhanced or enabled by the use of new graphene materials.
In 2008, graphene produced by exfoliation was one of the most expensive materials on Earth, with a sample with the area of the cross section of a human hair costing more than $1,000 as of April 2008 (about $100,000,000/cm). Since then, exfoliation procedures have been scaled up, and now companies sell graphene in large quantities. The price of epitaxial graphene on SiC is dominated by the substrate price, which was approximately $100/cm as of 2009.
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Hong and his team in South Korea pioneered the synthesis of large-scale graphene films using chemical vapour deposition (CVD) on thin nickel layers, which triggered research on practical applications, with wafer sizes up to 30 inches (760 mm) reported.
In 2013, the European Union made a €1 billion grant to be used for research into potential graphene applications. In 2013 the Graphene Flagship consortium formed, including Chalmers University of Technology and seven other European universities and research centers, along with Nokia. Nokia has also been working on graphene technology for several years.
Medicine
Graphene is reported to have enhanced PCR by increasing the yield of DNA product. Experiments revealed that graphene's thermal conductivity could be the main factor behind this result. Graphene yields DNA product equivalent to positive control with up to 65% reduction in PCR cycles.
Integrated circuits
For integrated circuits, graphene has a high carrier mobility, as well as low noise, allowing it to be used as the channel in a field-effect transistor. Single sheets of graphene are hard to produce and even harder to make on an appropriate substrate.
In 2008, the smallest transistor so far, one atom thick, 10 atoms wide was made of graphene. IBM announced in December 2008 that they had fabricated and characterized graphene transistors operating at GHz frequencies. In May 2009, an n-type transistor was announced meaning that both n and p-type graphene transistors had been created. A functional graphene integrated circuit was demonstrated – a complementary inverter consisting of one p- and one n-type graphene transistor. However, this inverter suffered from a very low voltage gain.
According to a January 2010 report, graphene was epitaxially grown on SiC in a quantity and with quality suitable for mass production of integrated circuits. At high temperatures, the quantum Hall effect could be measured in these samples. IBM built 'processors' using 100 GHz transistors on 2-inch (51 mm) graphene sheets.
In June 2011, IBM researchers announced that they had succeeded in creating the first graphene-based integrated circuit, a broadband radio mixer. The circuit handled frequencies up to 10 GHz. Its performance was unaffected by temperatures up to 127 C.
In June 2013 an 8 transistor 1.28 GHz ring oscillator circuit was described.
Transistors
Graphene exhibits a pronounced response to perpendicular external electric fields, potentially forming field-effect transistors (FET). A 2004 paper documented FETs with an on-off ratio of ~30 at room temperature. A 2006 paper announced an all-graphene planar FET with side gates. Their devices showed changes of 2% at cryogenic temperatures. The first top-gated FET (on–off ratio of <2) was demonstrated in 2007. Graphene nanoribbons may prove generally capable of replacing silicon as a semiconductor.
US patent 7015142 for graphene-based electronics was issued in 2006. In 2008, researchers at MIT Lincoln Lab produced hundreds of transistors on a single chip and in 2009, very high frequency transistors were produced at Hughes Research Laboratories.
A 2008 paper demonstrated a switching effect based on a reversible chemical modification of the graphene layer that gives an on–off ratio of greater than six orders of magnitude. These reversible switches could potentially be employed in nonvolatile memories.
In 2009, researchers demonstrated four different types of logic gates, each composed of a single graphene transistor.
Practical uses for these circuits are limited by the very small voltage gain they exhibit. Typically, the amplitude of the output signal is about 40 times less than that of the input signal. Moreover, none of these circuits operated at frequencies higher than 25 kHz.
In the same year, tight-binding numerical simulations demonstrated that the band-gap induced in graphene bilayer field effect transistors is not sufficiently large for high-performance transistors for digital applications, but can be sufficient for ultra-low voltage applications, when exploiting a tunnel-FET architecture.
In February 2010, researchers announced transistors with an on/off rate of 100 gigahertz, far exceeding the rates of previous attempts, and exceeding the speed of silicon transistors with an equal gate length. The 240 nm devices were made with conventional silicon-manufacturing equipment.
In November 2011, researchers used 3d printing (additive manufacturing) as a method for fabricating graphene devices.
In 2013, researchers demonstrated graphene's high mobility in a detector that allows broad band frequency selectivity ranging from the THz to IR region (0.76-33THz) A separate group created a terahertz-speed transistor with bistable characteristics, which means that the device can spontaneously switch between two electronic states. The device consists of two layers of graphene separated by an insulating layer of boron nitride a few atomic layers thick. Electrons move through this barrier by quantum tunneling. These new transistors exhibit “negative differential conductance,” whereby the same electrical current flows at two different applied voltages.
Graphene does not have an energy band-gap, which presents a hurdle for its applications in digital logic gates. The efforts to induce a band-gap in graphene via quantum confinement or surface functionalization have not resulted in a breakthrough. The negative differential resistance experimentally observed in graphene field-effect transistors of "conventional" design allows for construction of viable non-Boolean computational architectures with the gap-less graphene. The negative differential resistance — observed under certain biasing schemes — is an intrinsic property of graphene resulting from its symmetric band structure. The results present a conceptual change in graphene research and indicate an alternative route for graphene's applications in information processing.
In 2013 researchers reported the creation of transistors printed on flexible plastic that operate at 25-gigahertz, sufficient for communications circuits and that can be fabricated at scale. The researchers first fabricate the non-graphene-containing structures—the electrodes and gates—on plastic sheets. Separately, they grow large graphene sheets on metal, then peel it off and transfer it to the plastic. Finally, they top the sheet with a waterproof layer. The devices work after being soaked in water, and are flexible enough to be folded.
Redox
Graphene oxide can be reversibly reduced and oxidized using electrical stimulus. Controlled reduction and oxidation in two-terminal devices containing multilayer graphene oxide films are shown to result in switching between partially reduced graphene oxide and graphene, a process that modifies the electronic and optical properties. Oxidation and reduction are related to resistive switching.
Transparent conducting electrodes
Graphene's high electrical conductivity and high optical transparency make it a candidate for transparent conducting electrodes, required for such applications as touchscreens, liquid crystal displays, organic photovoltaic cells, and organic light-emitting diodes. In particular, graphene's mechanical strength and flexibility are advantageous compared to indium tin oxide, which is brittle. Graphene films may be deposited from solution over large areas.
Large-area, continuous, transparent and highly conducting few-layered graphene films were produced by chemical vapor deposition and used as anodes for application in photovoltaic devices. A power conversion efficiency (PCE) up to 1.71% was demonstrated, which is 55.2% of the PCE of a control device based on indium tin oxide.
Organic light-emitting diodes (OLEDs) with graphene anodes have been demonstrated. The electronic and optical performance of graphene-based devices are similar to devices made with indium tin oxide.
A carbon-based device called a light-emitting electrochemical cell (LEC) was demonstrated with chemically-derived graphene as the cathode and the conductive polymer PEDOT as the anode. Unlike its predecessors, this device contains only carbon-based electrodes, with no metal.
Ethanol distillation
Graphene oxide membranes allow water vapor to pass through, but are impermeable to other liquids and gases. This phenomenon has been used for further distilling of vodka to higher alcohol concentrations, in a room-temperature laboratory, without the application of heat or vacuum as used in traditional distillation methods. Further development and commercialization of such membranes could revolutionize the economics of biofuel production and the alcoholic beverage industry.
Desalination
Research suggests that graphene filters could outperform other techniques of desalination by a significant margin.
Solar cells
Graphene has a unique combination of high electrical conductivity and optical transparency, which make it a candidate for use in solar cells. A single sheet of graphene is a zero-bandgap semiconductor whose charge carriers are delocalized over large areas, implying that carrier scattering does not occur. Because this material only absorbs 2.3% of visible light, it is a candidate for applications requiring a transparent conductor. Graphene can be assembled into a film electrode with low roughness. However, graphene films produced via solution processing contain lattice defects and grain boundaries that act as recombination centers and decrease the material's electrical conductivity. Thus, these films must be made thicker than one atomic layer to obtain useful sheet resistances. This added resistance can be combatted by incorporating conductive filler materials, such as a silica matrix. Reduced graphene film's electrical conductivity can be improved by attaching large aromatic molecules such as pyrene-1-sulfonic acid sodium salt (PyS) and the disodium salt of 3,4,9,10-perylenetetracarboxylic diimide bisbenzenesulfonic acid (PDI). These molecules, under high temperatures, facilitate better π-conjugation of the graphene basal plane. Graphene films have high transparency in the visible and near-infrared regions and are chemically and thermally stable.
For graphene to be used in commercial solar cells, large-scale production are required. However, no scalable process for producing graphene is available, including the peeling of pyrolytic graphene or thermal decomposition of silicon carbide.
Graphene's high charge mobilities recommend it for use as a charge collector and transporter in photovoltaics (PV). Using graphene as a photoactive material requires its bandgap to be 1.4-1.9eV. In 2010, single cell efficiencies of nanostructured graphene-based PVs of over 12% were achieved. According to P. Mukhopadhyay and R. K. Gupta organic photovoltaics could be "devices in which semiconducting graphene is used as the photoactive material and metallic graphene is used as the conductive electrodes".
In 2010，Xinming Li and Hongwei Zhu from Tsinghua University first reported graphene-silicon heterojunction solar cell,where graphene served as a transparent electrode and introduced a built-in electric field near the interface between the graphene and n-type silicon to help collect photo-generated carriers.More studies promote this new type of photovoltaic device. For example，in 2012 researchers from the University of Florida reported efficiency of 8.6% for a prototype cell consisting of a wafer of silicon coated with a layer of graphene doped with trifluoromethanesulfonyl-amide (TFSA). Furthermore,Xinming Li found chemical doping could improve the graphene characteristics and significantly enhance the efficiency of graphene-silicon solar cell to 9.6% in 2013.
In 2013 another team claimed to have reached 15.6% percent using a combination of titanium oxide and graphene as a charge collector and perovskite as a sunlight absorber. The device is manufacturable at temperatures under 150 °C (302 °F) using solution-based deposition. This lowers production costs and offers the potential using flexible plastics.
Large scale production of highly transparent graphene films by chemical vapor deposition was achieved in 2008. In this process, ultra-thin graphene sheets are created by first depositing carbon atoms in the form of graphene films on a nickel plate from methane gas. A protective layer of thermoplastic is laid over the graphene layer and the nickel underneath is dissolved in an acid bath. The final step is to attach the plastic-protected graphene to a flexible polymer sheet, which can then be incorporated into an OPV cell. Graphene/polymer sheets range in size up to 150 square centimeters and can be used to create dense arrays of flexible OPV cells. It may eventually be possible to run printing presses covering extensive areas with inexpensive solar cells, much like newspaper presses print newspapers (roll-to-roll).
Silicon generates only one current-driving electron for each photon it absorbs, while graphene can produce multiple electrons. Solar cells made with graphene could offer 60% conversion efficiency – double the widely-accepted maximum efficiency of silicon cells.
Single-molecule gas detection
Theoretically graphene makes an excellent sensor due to its 2D structure. The fact that its entire volume is exposed to its surrounding makes it very efficient to detect adsorbed molecules. However, similar to carbon nanotubes, graphene has no dangling bonds on its surface. Gaseous molecules cannot be readily adsorbed onto graphene surfaces, so intrinsically graphene is insensitive. The sensitivity of graphene chemical gas sensors can be dramatically enhanced by functionalization, for example, coating the film with a thin layer of certain polymers. The thin polymer layer acts like a concentrator that absorbs gaseous molecules. The molecule absorption introduces a local change in electrical resistance of graphene sensors. While this effect occurs in other materials, graphene is superior due to its high electrical conductivity (even when few carriers are present) and low noise, which makes this change in resistance detectable.
Quantum dots
Graphene quantum dots (GQDs) keep all dimensions less than 10 nm. Their size and edge crystallography govern their electrical, magnetic, optical and chemical properties. GQDs can be produced via graphite nanotomy or via bottom-up, solution-based routes (Diels-Alder, cyclotrimerization and/or cyclodehydrogenation reactions). GQDs with controlled structure can be incorporated into applications in electronics, optoelectronics and electromagnetics. Quantum confinement can be created by changing the width of graphene nanoribbons (GNRs) at selected points along the ribbon.
Frequency multiplier
In 2009, researchers built experimental graphene frequency multipliers that take an incoming signal of a certain frequency and output a signal at a multiple of that frequency.
Optical modulator
When the Fermi level of graphene is tuned, its optical absorption can be changed. In 2011, researchers reported the first graphene-based optical modulator. Operating at 1.2 GHz without a temperature controller, this modulator has a broad bandwidth (from 1.3 to 1.6 μm) and small footprint (~25 μm).
Coolant additive
Graphene's high thermal conductivity suggests that it could be used as an additive in coolants. Preliminary research work showed that 5% graphene by volume can enhance the thermal conductivity of a base fluid by 86%. Another application due to graphene's enhanced thermal conductivity was found in PCR.
Reference material
Graphene's properties suggest it as a reference material for characterizing electroconductive and transparent materials. One layer of graphene absorbs 2.3% of white light.
This property was used to define the conductivity of transparency that combines sheet resistance and transparency. This parameter was used to compare materials without the use of two independent parameters.
Thermal management
In 2011, researchers reported that a three-dimensional, vertically aligned, functionalized multilayer graphene architecture can be an approach for graphene-based thermal interfacial materials (TIMs) with superior thermal conductivity and ultra-low interfacial thermal resistance between graphene and metal.
Graphene-metal composites can be utilized in thermal interface materials.
Energy storage
Supercapacitor
Due to graphene's high surface area to mass ratio, one potential application is in the conductive plates of supercapacitors.
In February 2013 researchers announced a novel technique to produce graphene supercapacitors based on the DVD burner reduction approach.
Electrode for Li-ion batteries
Stable Li-ion cycling has recently been demonstrated in bi- and few layer graphene films grown on nickel substrates, while single layer graphene films have been demonstrated as a protective layer against corrosion in battery components such as the battery case. This creates possibilities for flexible electrodes for microscale Li-ion batteries where the anode acts as the active material as well as the current collector.
There are also silicon-graphene anode Li-ion batteries.
Engineered piezoelectricity
Density functional theory simulations predict that depositing certain adatoms on graphene can render it piezoelectrically responsive to an electric field applied in the out-of-plane direction. This type of locally engineered piezoelectricity is similar in magnitude to that of bulk piezoelectric materials and makes graphene a candidate for control and sensing in nanoscale devices.
Biodevice
Graphene's modifiable chemistry, large surface area, atomic thickness and molecularly gatable structure make antibody-functionalized graphene sheets excellent candidates for mammalian and microbial detection and diagnosis devices.
The most ambitious biological application of graphene is for rapid, inexpensive electronic DNA sequencing. Integration of graphene (thickness of 0.34 nm) layers as nanoelectrodes into a nanopore can solve a bottleneck for nanopore-based single-molecule DNA sequencing.
On November 20, 2013 the Bill & Melinda Gates Foundation awarded $100,000 to 'to develop new elastic composite materials for condoms containing nanomaterials like graphene'.
Radio wave absorption
Stacked graphene layers on a quartz substrate increased the absorption of millimeter (radio) waves by 90 per cent over 125 – 165 GHz bandwidth, extensible to microwave and low-terahertz frequencies, while remaining transparent to visible light. For example, graphene could be used as a coating for buildings or windows to block radio waves. Absorption is a result of mutually coupled Fabry-Perot resonators represented by each graphene-quartz substrate. A repeated transfer-and-etch process was used to control surface resistivity.
Pseudo-relativistic theory
Graphene's electrical properties can be described by a conventional tight-binding model; in this model the energy of the electrons with wave vector k is
with the nearest-neighbor hopping energy γ0 ≈ 2.8 eV and the lattice constant a ≈ 2.46 Å. The conduction and valence band, respectively, correspond to the different signs in the above dispersion relation; they touch each other at six points, the "K-values". However, only two of these six points are independent, while the rest are equivalent by symmetry. In the vicinity of the K-points the energy depends linearly on the wave vector, similar to a relativistic particle. Since an elementary cell of the lattice has a basis of two atoms, the wave function even has an effective 2-spinor structure.
As a consequence, at low energies, even neglecting the true spin, the electrons can be described by an equation that is formally equivalent to the massless Dirac equation. This pseudo-relativistic description is restricted to the chiral limit, i.e., to vanishing rest mass M0, which leads to interesting additional features:
Here vF ~ 10 is the Fermi velocity in graphene, which replaces the velocity of light in the Dirac theory; is the vector of the Pauli matrices, is the two-component wave function of the electrons, and E is their energy.
is the vector of the 
is the two-component wave function of the electrons, and E is their energy.
See also
3References
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External links
- Graphene at The Periodic Table of Videos (University of Nottingham)
- Most of graphene papers published by Andre Geim's group are downloadable here
- Is Graphene the New Silicon? National Science Foundation, March 27, 2008
- "Band structure of graphene" (PDF). Retrieved 2009-08-15.
- Graphene portal with daily news and resources
- Castro Neto, Antonio H. (12 May 2009). "Pauling's dreams for graphene".
- Peres, N M R; Ribeiro, R M (2009). "Focus on Graphene". New Journal of Physics. 11 (9): 095002. Bibcode:2009NJPh...11i5002P. doi:10.1088/1367-2630/11/9/095002.
- Online short course: Colloquium on Graphene Physics and Devices
- List of Authority Articles on Graphene Theme
- Short video explanation 'What is Graphene?'
- Short video 'Graphene and the Carbon Revolution'
- 'Scientists Find Simple Way to Produce Graphene'
- 'Graphene technology moves closer'
- Graphene: Patent surge reveals global race
- 'What Graphene offers for future Electronic Devices by Linda Rae'
- 'Graphene Shows Promise: Researchers are Looking for New Materials that can take over where Silicon will Leave Off'
- 'Defects Improve Graphene Conductivity'
- 'IOP Science Graphene Articles
- (PDF) 'Engineering Controls for Nano-scale Graphene Platelets During Manufacturing and Handling Processes'
- Graphene, 15 September 2010, BBC Radio program Discovery
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