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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 article, the effects of site dilution disorder on the electronic properties in graphene multilayers, in particular the bilayer and the infinite stack, were studied. And the authors also studied the problem of impurities in the biased graphene bilayer.
Abstract: We study the effects of site dilution disorder on the electronic properties in graphene multilayers, in particular the bilayer and the infinite stack. The simplicity of the model allows for an easy implementation of the coherent-potential approximation and some analytical results. Within the model we compute the self-energies, the density of states, and the spectral functions. Moreover, we obtain the frequency and temperature dependence of the conductivity as well as the dc conductivity. The $c$-axis response is unconventional in the sense that impurities increase the response for low enough doping. We also study the problem of impurities in the biased graphene bilayer.

245 citations


Additional excerpts

  • ..., 2007b) to transistors (Nilsson et al., 2008)....

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Journal ArticleDOI
TL;DR: D-dimensional polymerized membranes embedded in d dimensions using a self-consistent screening approximation yields identical lower critical dimension for the flat phase and crumpling transition.
Abstract: We study D-dimensional polymerized membranes embedded in d dimensions using a self-consistent screening approximation. It is exact for large d to order 1/d, for any d to order \ensuremath{\epsilon}=4-D, and for d=D. For flat physical membranes (D=2, d=3) it predicts a roughness exponent \ensuremath{\zeta}=0.590. For phantom membranes at the crumpling transition the size exponent is \ensuremath{ u}=0.732. It yields identical lower critical dimension for the flat phase and crumpling transition ${\mathit{D}}_{\mathrm{lc}}$(d)=2d/(d+1) (${\mathit{D}}_{\mathrm{lc}}$= \ensuremath{\surd}2 for codimension 1). For physical membranes with random quenched curvature \ensuremath{\zeta}=0.775 in the new T=0 flat phase in good agremeent with simulations.

244 citations

Journal ArticleDOI
TL;DR: It is shown that the quasiparticle decay rate has a minimum as a function of energy, there is a universal minimum value for the in-plane conductivity of order e(2)/h per plane and, unexpectedly, the c-axis conductivity is enhanced by disorder at low doping, leading to an enormous conductivity anisotropy at low temperatures.
Abstract: We study the effects of disorder in the electronic properties of graphene multilayers, with special focus on the bilayer and the infinite stack. At low energies and long wavelengths, the electronic self-energies and density of states exhibit behavior with divergences near half filling. As a consequence, the spectral functions and the conductivities acquire anomalous properties. In particular, we show that the quasiparticle decay rate has a minimum as a function of energy, there is a universal minimum value for the in-plane conductivity of order e(2)/h per plane and, unexpectedly, the c-axis conductivity is enhanced by disorder at low doping, leading to an enormous conductivity anisotropy at low temperatures.

244 citations


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

  • ...The interband ex hangeenergy is redu ed in a bilayer (Nilsson et al., 2006 ), anda positive ontribution that depends logarithmi ally onthe bandwidth in graphene is absent in its bilayer....

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  • ...Furthermore, a ording to Hartree-Fo k al ulations, lean bilayer graphene is unstable towardsferromagnetism (Nilsson et al., 2006b).1....

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  • ...The same result, namely a ondu tan e of the order of e2/h, is obtained for disordered graphene bilayers where aself- onsistent al ulation leads to universal ondu tivityat the neutrality point (Katsnelson, 2007 ; Nilsson et al.,2006a, 2007a)....

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  • ...Higherorder orre tions to (227) lead to a rst order transitionat slightly higher densities (Nilsson et al., 2006 )....

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  • ...Hen e, even in a leansystem, the number of ondu ting hannels in the dire -tion perpendi ular to the layers vanishes at zero energy(Nilsson et al., 2006a, 2007a)....

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Journal ArticleDOI
TL;DR: In this paper, the edge states of graphene ribbons in the quantized Hall regime were studied, and they can be described within a continuum model (the Dirac equation) when appropriate boundary conditions are adopted.
Abstract: We study edges states of graphene ribbons in the quantized Hall regime, and show that they can be described within a continuum model (the Dirac equation) when appropriate boundary conditions are adopted. The two simplest terminations, zigzag and armchair edges, are studied in detail. For zigzag edges, we find that the lowest-Landau-level states terminate in two types of edge states, dispersionless and current-carrying surface states. The latter involve components on different sublattices that may be separated by distances far greater than the magnetic length. For armchair edges, the boundary conditions are met by admixing states from different valleys, and we show that this leads to a single set of edges states for the lowest Landau level and two sets for all higher Landau levels. In both cases, the resulting Hall conductance step for the lowest Landau level is half that between higher Landau levels, as observed in experiment.

243 citations


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

  • ...The wavefun tions in the dis rete latti e must be real,and at large distan es the a tual solution found neara va an y tends to a superposition of two solutionsformed from wavefun tions from the two valleys withequal weight, in a way similar to the mixing at arm hairedges (Brey and Fertig, 2006b)....

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  • ...The spe trum of graphene nanoribbonsThe spe trum of graphene nanoribbons depend verymu h on the nature of their edges zigzag or arm hair(Brey and Fertig, 2006a,b; Nakada et al., 1996)....

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  • ...This was originally done both with and without amagneti eld (Brey and Fertig, 2006a,b; Nakada et al.,1996).1....

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Journal ArticleDOI
TL;DR: In this article, a scanning tunneling spectroscopy (STS) study of the local electronic structure of single and bilayer graphene grown epitaxially on a SiC(0001) surface is presented.
Abstract: We present a scanning tunneling spectroscopy (STS) study of the local electronic structure of single and bilayer graphene grown epitaxially on a SiC(0001) surface. Low voltage topographic images reveal fine, atomic-scale carbon networks, whereas higher bias images are dominated by emergent spatially inhomogeneous large-scale structure similar to a carbon-rich reconstruction of SiC(0001). STS spectroscopy shows a ~100meV gap-like feature around zero bias for both monolayer and bilayer graphene/SiC, as well as significant spatial inhomogeneity in electronic structure above the gap edge. Nanoscale structure at the SiC/graphene interface is seen to correlate with observed electronic spatial inhomogeneity. These results are important for potential devices involving electronic transport or tunneling in graphene/SiC.

242 citations