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Journal ArticleDOI

The electronic properties of graphene

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.
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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Citations
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Journal ArticleDOI
TL;DR: This work reviews the historical development of Transition metal dichalcogenides, methods for preparing atomically thin layers, their electronic and optical properties, and prospects for future advances in electronics and optoelectronics.
Abstract: Single-layer metal dichalcogenides are two-dimensional semiconductors that present strong potential for electronic and sensing applications complementary to that of graphene.

13,348 citations

Journal ArticleDOI
19 Jun 2009-Science
TL;DR: This review analyzes recent trends in graphene research and applications, and attempts to identify future directions in which the field is likely to develop.
Abstract: Graphene is a wonder material with many superlatives to its name. It is the thinnest known material in the universe and the strongest ever measured. Its charge carriers exhibit giant intrinsic mobility, have zero effective mass, and can travel for micrometers without scattering at room temperature. Graphene can sustain current densities six orders of magnitude higher than that of copper, shows record thermal conductivity and stiffness, is impermeable to gases, and reconciles such conflicting qualities as brittleness and ductility. Electron transport in graphene is described by a Dirac-like equation, which allows the investigation of relativistic quantum phenomena in a benchtop experiment. This review analyzes recent trends in graphene research and applications, and attempts to identify future directions in which the field is likely to develop.

12,117 citations

Journal ArticleDOI
TL;DR: Topological superconductors are new states of quantum matter which cannot be adiabatically connected to conventional insulators and semiconductors and are characterized by a full insulating gap in the bulk and gapless edge or surface states which are protected by time reversal symmetry.
Abstract: Topological insulators are new states of quantum matter which cannot be adiabatically connected to conventional insulators and semiconductors. They are characterized by a full insulating gap in the bulk and gapless edge or surface states which are protected by time-reversal symmetry. These topological materials have been theoretically predicted and experimentally observed in a variety of systems, including HgTe quantum wells, BiSb alloys, and Bi2Te3 and Bi2Se3 crystals. Theoretical models, materials properties, and experimental results on two-dimensional and three-dimensional topological insulators are reviewed, and both the topological band theory and the topological field theory are discussed. Topological superconductors have a full pairing gap in the bulk and gapless surface states consisting of Majorana fermions. The theory of topological superconductors is reviewed, in close analogy to the theory of topological insulators.

11,092 citations

Journal ArticleDOI
TL;DR: An overview of the synthesis, properties, and applications of graphene and related materials (primarily, graphite oxide and its colloidal suspensions and materials made from them), from a materials science perspective.
Abstract: There is intense interest in graphene in fields such as physics, chemistry, and materials science, among others. Interest in graphene's exceptional physical properties, chemical tunability, and potential for applications has generated thousands of publications and an accelerating pace of research, making review of such research timely. Here is an overview of the synthesis, properties, and applications of graphene and related materials (primarily, graphite oxide and its colloidal suspensions and materials made from them), from a materials science perspective.

8,919 citations

Journal ArticleDOI
TL;DR: This Review describes how the tunable electronic structure of TMDs makes them attractive for a variety of applications, as well as electrically active materials in opto-electronics.
Abstract: Ultrathin two-dimensional nanosheets of layered transition metal dichalcogenides (TMDs) are fundamentally and technologically intriguing. In contrast to the graphene sheet, they are chemically versatile. Mono- or few-layered TMDs - obtained either through exfoliation of bulk materials or bottom-up syntheses - are direct-gap semiconductors whose bandgap energy, as well as carrier type (n- or p-type), varies between compounds depending on their composition, structure and dimensionality. In this Review, we describe how the tunable electronic structure of TMDs makes them attractive for a variety of applications. They have been investigated as chemically active electrocatalysts for hydrogen evolution and hydrosulfurization, as well as electrically active materials in opto-electronics. Their morphologies and properties are also useful for energy storage applications such as electrodes for Li-ion batteries and supercapacitors.

7,903 citations

References
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Journal ArticleDOI
TL;DR: In this paper, the effect of electron-electron interactions in the electronic properties of a biased graphene bilayer was studied and it was shown that due to the unusual topology of the Fermi surface, electron and electron interactions are greatly enhanced.
Abstract: We study the effect of electron-electron interactions in the electronic properties of a biased graphene bilayer. This system is a semiconductor with conduction and valence bands characterized by an unusual ``Mexican-hat'' dispersion. We focus on the metallic regime where the chemical potential lies in the Mexican hat in the conduction band, leading to a topologically non trivial Fermi surface in the shape of a ring. We show that due to the unusual topology of the Fermi surface, electron-electron interactions are greatly enhanced. We show that the ferromagnetic instability can occur provided a low density of carriers. We compute the electronic polarization function in the random-phase approximation and show that while at low energies the system behaves as a Fermi liquid (albeit with peculiar Friedel oscillations), at high frequencies it shows a highly anomalous response when compared to ordinary metals.

60 citations


Additional excerpts

  • ...The analysis des ribed above an be extended to thebiased bilayer, where a gap separates the ondu tion andvalen e bands (Stauber et al., 2007)....

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  • ...valence bands (Stauber et al., 2007)....

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Journal ArticleDOI
TL;DR: In this paper, both numerical and analytical studies of graphene roughness with a crystal structure including $500\ifmmode\times\else\texttimes\fi{}500$ atoms were presented.
Abstract: We present both numerical and analytical studies of graphene roughness with a crystal structure including $500\ifmmode\times\else\texttimes\fi{}500$ atoms. The roughness can effectively result in a random gauge field and has important consequences for its electronic structure. Our results show that its height fluctuations in small scales have a scaling behavior with a temperature dependent roughness exponent in the interval of $0.6l\ensuremath{\chi}l0.7$. The correlation function of height fluctuations depends on temperature with a characteristic length scale of $\ensuremath{\approx}90\phantom{\rule{0.3em}{0ex}}\mathrm{\AA{}}$ (at room temperature). We show that the correlation function of the induced gauge field has a short-range nature with a correlation length of about $\ensuremath{\simeq}2\char21{}3\phantom{\rule{0.3em}{0ex}}\mathrm{\AA{}}$. We also treat the problem analytically by using the Martin-Siggia-Rose method. The renormalization group flows did not yield any delocalized-localized transition arising from the graphene roughness. Our results are in good agreement with recent experimental observations.

60 citations

Journal ArticleDOI
TL;DR: In this article, the authors present a theoretical description of the electronic properties of graphene in the presence of disorder, electron-electron interactions, and particle-hole symmetry breaking, and show that while particlehole asymmetry and long-range Coulomb interactions lead to the phenomenon of self-doping, local defects determine the transport and spectroscopic properties.

60 citations


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

  • ...Let us now fo us on the opti al ondu tivity, σxx(ω)(Gusynin et al., 2007; Peres et al., 2006 )....

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  • ...(Peres et al., 2006 )....

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  • ...…on line) Energy spe trum (in units of t) for agraphene ribbon 600a wide, as a fun tion of the momentum k along the ribbon (in units of 1/(√3a)), in the presen e of on ning potential with V0 = 1 eV, λ = 180a.Consider the tight-binding des ription (Chen et al.,2007a; Peres et al., 2006b) of Se ....

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  • ...(203)and (204) redu e to: σ0 = 4 π e2 h , (205)whi h is the so- alled universal ondu tivity of graphene(Fradkin, 1986a,b; Katsnelson, 2006b; Lee, 1993;Ludwig et al., 1994; Nersesyan et al., 1994; Peres et al.,2006 ; Tworzydlo et al., 2006; Yang and Nayak, 2002;Ziegler, 1998)....

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  • ...…Dira fermions in a magneti eld (in luding disorder) an be written as: H = H0+Hiwhere H0 is given by (5) and Hi is the impurity potentialreading (Peres et al., 2006 ): Hi = V Ni ∑ j=1 δ(r − rj)I (192)The formulation of the problem in se ond quantizationrequires the solution of H0, whi h was…...

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Journal ArticleDOI
TL;DR: It is argued that the specific heat of N massless Dirac fermions in two spatial dimensions interacting with 1/r Coulomb interactions is suppressed logarithmically relative to its noninteracting counterpart, and its dependence on the dielectric constant is calculated analytically.
Abstract: It is argued that the specific heat of N massless Dirac fermions in two spatial dimensions interacting with 1/r Coulomb interactions is suppressed logarithmically relative to its noninteracting counterpart. The (dimensionless) coefficient of the logarithm is calculated in a closed form in the leading order in large N expansion, but to all orders in the effective fine structure constant, alpha(F), a procedure which takes into account finite temperature screening. This effect is expected to occur in a single-layer graphene embedded in a dielectric medium. Its dependence on the dielectric constant is calculated analytically.

60 citations


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

  • ...Other thermodynami properties of undoped and doped graphene an also be al ulated (Barlas et al., 2007; Vafek, 2007)....

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Journal ArticleDOI
01 Dec 2007-EPL
TL;DR: In this paper, exact analytical and numerical results for the electronic spectra and the Friedel oscillations around a substitutional impurity atom in a graphene lattice were presented, where the authors employ a T-matrix formalism and find that disorder in the hopping introduces additional interference terms around the impurity.
Abstract: We present exact analytical and numerical results for the electronic spectra and the Friedel oscillations around a substitutional impurity atom in a graphene lattice. A chemical dopant in graphene introduces changes in the on-site potential as well as in the hopping amplitude. We employ a T-matrix formalism and find that disorder in the hopping introduces additional interference terms around the impurity that can be understood in terms of bound, semi-bound, and unbound processes for the Dirac electrons. These interference effects can be detected by scanning tunneling microscopy.

60 citations


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

  • ...…2002; Dresselhaus et al.,1983; Tanuma and Kamimura, 1985)); in orporation ofnitrogen and/and boron in its stru ture (Martins et al.,2007; Peres et al., 2007a) (in analogy with what hasbeen done in nanotubes (Stephan et al., 1994)); usingdi erent substrates that modify the ele troni stru…...

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  • ...…based on s reened harged impurities it ispossible to obtain from a Boltzmann equation ap-proa h a ondu tivity varying linearly with the den-sity, in agreement with the experimental result (Ando,2006b; Katsnelson and Geim, 2008; Novikov, 2007b;Peres et al., 2007b; Trushin and S hliemann, 2007)....

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