The electronic properties of graphene

doi:10.1103/REVMODPHYS.81.109

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The electronic properties of graphene

Journal Article•DOI•

The electronic properties of graphene

A. H. Castro Neto¹, Francisco Guinea², Nuno M. R. Peres³, Kostya S. Novoselov⁴, Andre K. Geim⁴ - Show less +1 more•Institutions (4)

Boston University¹, Spanish National Research Council², University of Minho³, University of Manchester⁴

14 Jan 2009-Reviews of Modern Physics (American Physical Society)-Vol. 81, Iss: 1, pp 109-162

TL;DR: In this paper, the basic theoretical aspects of graphene, a one-atom-thick allotrope of carbon, with unusual two-dimensional Dirac-like electronic excitations, are discussed.

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Abstract: This article reviews the basic theoretical aspects of graphene, a one-atom-thick allotrope of carbon, with unusual two-dimensional Dirac-like electronic excitations. The Dirac electrons can be controlled by application of external electric and magnetic fields, or by altering sample geometry and/or topology. The Dirac electrons behave in unusual ways in tunneling, confinement, and the integer quantum Hall effect. The electronic properties of graphene stacks are discussed and vary with stacking order and number of layers. Edge (surface) states in graphene depend on the edge termination (zigzag or armchair) and affect the physical properties of nanoribbons. Different types of disorder modify the Dirac equation leading to unusual spectroscopic and transport properties. The effects of electron-electron and electron-phonon interactions in single layer and multilayer graphene are also presented.

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Journal Article•DOI•

A manufacturing perspective on graphene dispersions

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David W. Johnson¹, Ben P. Dobson¹, Karl S. Coleman¹•Institutions (1)

Durham University¹

01 Oct 2015-Current Opinion in Colloid and Interface Science

TL;DR: In this paper, the effect of shear, solvent and chemical modification on the dispersion of graphene (including graphene oxide and reduced graphene oxide) is discussed in the context of manufacturing and commercialisation.

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Abstract: Harnessing the exceptional physical properties of graphene often requires its dispersion into aqueous or organic media. Dispersion must be achieved at a concentration and stability appropriate to the final application. However, the strong interaction between graphene sheets means it disperses poorly in all but a few high boiling organic solvents. This review presents an overview of graphene dispersion applications and a discussion of dispersion strategies: in particular the effect of shear, solvent and chemical modification on the dispersion of graphene (including graphene oxide and reduced graphene oxide). These techniques are discussed in the context of manufacturing and commercialisation.

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319 citations

Cites background from "The electronic properties of graphe..."

...atom thick [4], ballistic transport of electrons [5,6], absorption of 2% of the light passing through it [7], and being “the strongest material ever measured” [8] with a Young's modulus of TPa....
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Journal Article•DOI•

Nanocarbons for Biology and Medicine: Sensing, Imaging, and Drug Delivery

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Nishtha Panwar¹, Alana Mauluidy Soehartono¹, Kok Ken Chan¹, Shuwen Zeng², Shuwen Zeng¹, Gaixia Xu³, Junle Qu³, Philippe Coquet⁴, Philippe Coquet², Ken-Tye Yong¹, Xiaoyuan Chen⁵ - Show less +7 more•Institutions (5)

Nanyang Technological University¹, Centre national de la recherche scientifique², Shenzhen University³, Lille University of Science and Technology⁴, National Institutes of Health⁵

09 Jul 2019-Chemical Reviews

TL;DR: This review introduces the different carbon allotropes that can be used for theranostic applications with their respective preparation and surface functionalization approaches as well as their physical and chemical properties, and outlines the design considerations for nanocarbon materials as the key unifying themes.

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Abstract: Nanocarbons with different dimensions (e.g., 0D fullerenes and carbon nanodots, 1D carbon nanotubes and graphene nanoribbons, 2D graphene and graphene oxides, and 3D nanodiamonds) have attracted enormous interest for applications ranging from electronics, optoelectronics, and photovoltaics to sensing, bioimaging, and therapeutics due to their unique physical and chemical properties. Among them, nanocarbon-based theranostics (i.e., therapeutics and diagnostics) is one of the most intensively studied applications, as these nanocarbon materials serve as excellent biosensors, versatile drug/gene carriers for specific targeting in vivo, effective photothermal nanoagents for cancer therapy, and promising fluorescent nanolabels for cell and tissue imaging. This review provides a systematic overview of the latest theranostic applications of nanocarbon materials with a comprehensive comparison of the characteristics of different nanocarbon materials and their influences on theranostic applications. We first introduce the different carbon allotropes that can be used for theranostic applications with their respective preparation and surface functionalization approaches as well as their physical and chemical properties. Theranostic applications are described separately for both in vitro and in vivo systems by highlighting the protocols and the studied biosystems, followed by the toxicity and biodegradability implications. Finally, this review outlines the design considerations for nanocarbon materials as the key unifying themes that will serve as a foundational first principle for researchers to study, investigate, and generate effective, biocompatible, and nontoxic nanocarbon materials-based models for cancer theranostics applications. Finally, we summarize the review with an outlook on the challenges and novel theranostic protocols using nanocarbon materials for hard-to-treat cancers and other diseases. This review intends to present a comprehensive guideline for researchers in nanotechnology and biomedicine on the selection strategy of nanocarbon materials according to their specific requirements.

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318 citations

Journal Article•DOI•

Strong Coulomb drag and broken symmetry in double-layer graphene

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Roman V. Gorbachev¹, Andre K. Geim¹, Mikhail I. Katsnelson², K. S. Novoselov¹, T. Tudorovskiy², Irina V. Grigorieva¹, Allan H. MacDonald³, Sergey V. Morozov¹, Kenji Watanabe⁴, T. Taniguchi⁴, Leonid Ponomarenko¹ - Show less +7 more•Institutions (4)

University of Manchester¹, Radboud University Nijmegen², University of Texas at Austin³, National Institute for Materials Science⁴

01 Dec 2012-Nature Physics

TL;DR: In this paper, the Coulomb drag in the regime of weak to intermediate (d l) coupling was studied experimentally, where d is the interlayer separation and l is the characteristic distance between charge carriers, where the two Dirac liquids effectively nest within the same plane but can still be tuned and measured independently.

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Abstract: C oulomb drag is a frictional coupling between electric currents flowing in spatially separated conducting layers. It is caused by interlayer electron‐electron interactions. Previously, only the regime of weak (d l) to intermediate (d l) coupling could be studied experimentally, where d is the interlayer separation and l is the characteristic distance between charge carriers. Here we use graphene‐boron-nitride heterostructures withd down to 1 nm to probe Coulomb drag in the limitd l such that the two Dirac liquids effectively nest within the same plane, but can still be tuned and measured independently. The strongly interacting regime reveals many unexpected features. In particular, although drag vanishes because of electron‐hole symmetry when either layer is neutral, we often find drag strongest when both layers are neutral. Under this circumstance, drag is positive in zero magnetic field but changes its sign and rapidly grows in strength with field. The drag remains strong at room temperature. The broken electron‐hole symmetry is attributed to mutual polarization of closely spaced interacting layers.

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318 citations

Journal Article•DOI•

Compression behavior of single-layer graphenes.

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Otakar Frank, Georgia Tsoukleri¹, John Parthenios¹, Konstantinos Papagelis¹, Ibtsam Riaz², Rashid Jalil², Kostya S. Novoselov, Costas Galiotis¹ - Show less +4 more•Institutions (2)

University of Patras¹, University of Manchester²

24 May 2010-ACS Nano

TL;DR: The results show that graphenes embedded in plastic beams exhibit remarkable compression buckling strains, and calculations based on classical Euler analysis show that the buckling strain enhancement provided by the polymer lateral support is more than 6 orders of magnitude compared to that of suspended graphene in air.

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Abstract: Central to most applications involving monolayer graphenes is its mechanical response under various stress states. To date most of the work reported is of theoretical nature and refers to tension and compression loading of model graphenes. Most of the experimental work is indeed limited to the bending of single flakes in air and the stretching of flakes up to typically ∼1% using plastic substrates. Recently we have shown that by employing a cantilever beam we can subject single graphenes to various degrees of axial compression. Here we extend this work much further by measuring in detail both stress uptake and compression buckling strain in single flakes of different geometries. In all cases the mechanical response is monitored by simultaneous Raman measurements through the shift of either the G or 2D phonons of graphene. Despite the infinitely small thickness of the monolayers, the results show that graphenes embedded in plastic beams exhibit remarkable compression buckling strains. For large length (l)-...

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317 citations

Cites background from "The electronic properties of graphe..."

...further effectively modified by stress/strain.(5,6) In fact, strain engineering...
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...18 GPa nm(3).(5,16) The above eq 1 is mainly valid for suspended thin films and yields extremely small ( 10 (9)) c values for graphene monolayers of thicknesses of the order of atomic radii....
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Journal Article•DOI•

Direct formation of wafer scale graphene thin layers on insulating substrates by chemical vapor deposition.

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Ching Yuan Su¹, Ang-Yu Lu¹, Ang-Yu Lu², Chih-Yu Wu¹, Yi Te Li³, Keng-Ku Liu¹, Wenjing Zhang¹, Shi Yen Lin¹, Zheng Yu Juang¹, Yuan Liang Zhong³, Fu-Rong Chen², Lain-Jong Li¹, Lain-Jong Li⁴ - Show less +9 more•Institutions (4)

Academia Sinica¹, National Tsing Hua University², Chung Yuan Christian University³, National Chiao Tung University⁴

15 Aug 2011-Nano Letters

TL;DR: In a chemical vapor deposition process the carbon species dissociated on Cu surfaces not only result in graphene layers on top of the catalytic Cu thin films but also diffuse through Cu grain boundaries to the interface between Cu and underlying dielectrics.

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Abstract: Direct formation of high-quality and wafer scale graphenethinlayersoninsulatinggatedielectricssuchasSiO2is emergent for graphene electronics using Si-wafer compatible fabrication. Here, we report that in a chemical vapor deposition process the carbon species dissociated on Cu surfaces not only resultingraphenelayersontopofthecatalyticCuthin filmsbut also diffuse through Cu grain boundaries to the interface between Cu and underlying dielectrics. Optimization of the process parameters leads to a continuous and large-area gra- phene thin layers directly formed on top of the dielectrics. The bottom-gated transistor characteristics for the graphene films have shown quite comparable carrier mobility compared to the top-layer graphene. The proposed method allows us to achieve wafer-sized graphene on versatile insulating substrates without the need of graphene transfer.

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316 citations

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References

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Journal Article•DOI•

Electric Field Effect in Atomically Thin Carbon Films

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Kostya S. Novoselov¹, Andre K. Geim¹, Sergey V. Morozov, Da Jiang¹, Y. Zhang¹, S. V. Dubonos, Irina V. Grigorieva¹, A. A. Firsov - Show less +4 more•Institutions (1)

University of Manchester¹

22 Oct 2004-Science

TL;DR: Monocrystalline graphitic films are found to be a two-dimensional semimetal with a tiny overlap between valence and conductance bands and they exhibit a strong ambipolar electric field effect.

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Abstract: We describe monocrystalline graphitic films, which are a few atoms thick but are nonetheless stable under ambient conditions, metallic, and of remarkably high quality. The films are found to be a two-dimensional semimetal with a tiny overlap between valence and conductance bands, and they exhibit a strong ambipolar electric field effect such that electrons and holes in concentrations up to 10 13 per square centimeter and with room-temperature mobilities of ∼10,000 square centimeters per volt-second can be induced by applying gate voltage.

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55,532 citations

"The electronic properties of graphe..." refers background in this paper

...Be ause the DC magnetotransport properties ofgraphene are normally measured with the possibilityof tuning its ele troni density by a gate potential(Novoselov et al., 2004), it is important to ompute the ondu tivity kernel, sin e this has dire t experimentalrelevan e....
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...The same polarizability describes the screening of an external field perpendicular to the layers, like the one induced by a gate in electrically doped systems (Novoselov et al., 2004)....
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...Because the DC magnetotransport properties of graphene are normally measured with the possibility of tuning its electronic density by a gate potential (Novoselov et al., 2004), it is important to compute the conductivity kernel, since this has direct experimental relevance....
[...]
...…studies of graphene sta ks have showed that, within reasing number of layers, the system be omes in reas-ingly metalli ( on entration of harge arriers at zero en-ergy gradually in reases), and there appear several typesof ele tron-and-hole-like arries (Morozov et al., 2005;Novoselov et al., 2004)....
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...The same polarizabilitydes ribes the s reening of an external eld perpendi ularto the layers, like the one indu ed by a gate in ele tri- ally doped systems (Novoselov et al., 2004)....
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Journal Article•DOI•

The rise of graphene

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Andre K. Geim¹, Kostya S. Novoselov¹•Institutions (1)

University of Manchester¹

01 Mar 2007-Nature Materials

TL;DR: Owing to its unusual electronic spectrum, graphene has led to the emergence of a new paradigm of 'relativistic' condensed-matter physics, where quantum relativistic phenomena can now be mimicked and tested in table-top experiments.

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Abstract: Graphene is a rapidly rising star on the horizon of materials science and condensed-matter physics. This strictly two-dimensional material exhibits exceptionally high crystal and electronic quality, and, despite its short history, has already revealed a cornucopia of new physics and potential applications, which are briefly discussed here. Whereas one can be certain of the realness of applications only when commercial products appear, graphene no longer requires any further proof of its importance in terms of fundamental physics. Owing to its unusual electronic spectrum, graphene has led to the emergence of a new paradigm of 'relativistic' condensed-matter physics, where quantum relativistic phenomena, some of which are unobservable in high-energy physics, can now be mimicked and tested in table-top experiments. More generally, graphene represents a conceptually new class of materials that are only one atom thick, and, on this basis, offers new inroads into low-dimensional physics that has never ceased to surprise and continues to provide a fertile ground for applications.

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35,293 citations

"The electronic properties of graphe..." refers background in this paper

...As the current status of the experiment and potential applications have recently been reviewed (Geim and Novoselov, 2007), in this article we mostly concentrate on the theory and more technical aspects of electronic properties of this exciting new material....
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...As the urrent status of the experimentand potential appli ations have re ently been reviewed(Geim and Novoselov, 2007), in this arti le we mostly on entrate on the theory and more te hni al aspe ts ofele troni properties of this ex iting new material....
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...It has also been suggested that Coulomb intera tionsare onsiderably enhan ed in smaller geometries, su has graphene quantum dots (Milton Pereira Junior et al.,2007), leading to unusual Coulomb blo kade e e ts 4(Geim and Novoselov, 2007) and perhaps to magneti phenomena su h as the Kondo e e t....
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...…most versatile systems in ondensedmatter resear h.Besides the unusual basi properties, graphene hasthe potential for a large number of appli ations(Geim and Novoselov, 2007), from hemi al sensors(Chen et al., 2007 ; S hedin et al., 2007) to transistors(Nilsson et al., 2007b; Oostinga et al.,…...
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...Besides the unusual basic properties, graphene has the potential for a large number of applications (Geim and Novoselov, 2007), from chemical sensors (Chen et al....
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Book•

Theory of elasticity

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Stephen P. Timoshenko, James Norman Goodier

01 Jan 1934

TL;DR: The theory of the slipline field is used in this article to solve the problem of stable and non-stressed problems in plane strains in a plane-strain scenario.

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Abstract: Chapter 1: Stresses and Strains Chapter 2: Foundations of Plasticity Chapter 3: Elasto-Plastic Bending and Torsion Chapter 4: Plastic Analysis of Beams and Frames Chapter 5: Further Solutions of Elasto-Plastic Problems Chapter 6: Theory of the Slipline Field Chapter 7: Steady Problems in Plane Strain Chapter 8: Non-Steady Problems in Plane Strain

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20,724 citations

Journal Article•DOI•

Two-dimensional gas of massless Dirac fermions in graphene

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Kostya S. Novoselov¹, A. K. Geim¹, Sergey V. Morozov, Da Jiang¹, Mikhail I. Katsnelson², Irina V. Grigorieva¹, S. V. Dubonos, A. A. Firsov - Show less +4 more•Institutions (2)

University of Manchester¹, Radboud University Nijmegen²

10 Nov 2005-Nature

TL;DR: This study reports an experimental study of a condensed-matter system (graphene, a single atomic layer of carbon) in which electron transport is essentially governed by Dirac's (relativistic) equation and reveals a variety of unusual phenomena that are characteristic of two-dimensional Dirac fermions.

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Abstract: Quantum electrodynamics (resulting from the merger of quantum mechanics and relativity theory) has provided a clear understanding of phenomena ranging from particle physics to cosmology and from astrophysics to quantum chemistry. The ideas underlying quantum electrodynamics also influence the theory of condensed matter, but quantum relativistic effects are usually minute in the known experimental systems that can be described accurately by the non-relativistic Schrodinger equation. Here we report an experimental study of a condensed-matter system (graphene, a single atomic layer of carbon) in which electron transport is essentially governed by Dirac's (relativistic) equation. The charge carriers in graphene mimic relativistic particles with zero rest mass and have an effective 'speed of light' c* approximately 10(6) m s(-1). Our study reveals a variety of unusual phenomena that are characteristic of two-dimensional Dirac fermions. In particular we have observed the following: first, graphene's conductivity never falls below a minimum value corresponding to the quantum unit of conductance, even when concentrations of charge carriers tend to zero; second, the integer quantum Hall effect in graphene is anomalous in that it occurs at half-integer filling factors; and third, the cyclotron mass m(c) of massless carriers in graphene is described by E = m(c)c*2. This two-dimensional system is not only interesting in itself but also allows access to the subtle and rich physics of quantum electrodynamics in a bench-top experiment.

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18,958 citations

"The electronic properties of graphe..." refers background or methods in this paper

...This amazing re-sult has been observed experimentally (Novoselov et al.,2005a; Zhang et al., 2005) as shown in Fig.20....
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...Adapted from(Novoselov et al., 2005a)....
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...Adapted from (Novoselov et al.,2005a).and hen e σxy,inc. = I/VH = ±4Ne2/h, whi h is thenaive expe tation....
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...The period of os illations ∆n = 4B/Φ0,where B is the applied eld and Φ0 is the ux quantum(Novoselov et al., 2005a).or equivalently: (Oσ+ + O†σ−)φ = (2E/ωc)φ , (100)where σ± = σx ± iσy, and we have de ned the dimen-sionless length s ale: ξ = y ℓB − ℓBk , (101)and 1D harmoni os illator operators: O =…...
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...…invery unusual ways when ompared to ordinary ele tronsif subje ted to magneti elds, leading to new physi alphenomena (Gusynin and Sharapov, 2005; Peres et al.,2006 ) su h as the anomalous integer quantum Hall ef-fe t (IQHE) measured experimentally (Novoselov et al.,2005a; Zhang et al., 2005)....
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