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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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
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
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
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
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
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TL;DR: A comparison with the calculated local density of states at the surface layers allows us to identify Kish graphite as bulk graphite and HOPG as graphite with a finite thickness of 40 layers, which explains the qualitative difference between the two graphites reported in the recent transport measurements which suggested the quantum-Hall effect in HopG.
Abstract: Scanning tunneling spectroscopy (STS) measurements were made on surfaces of two different kinds of graphite samples, Kish graphite and highly oriented pyrolytic graphite (HOPG), at very low temperatures and in high magnetic fields. We observed a series of peaks in the tunnel spectra associated with Landau quantization of the quasi-two-dimensional electrons and holes. A comparison with the calculated local density of states at the surface layers allows us to identify Kish graphite as bulk graphite and HOPG as graphite with a finite thickness of 40 layers. This explains the qualitative difference between the two graphites reported in the recent transport measurements which suggested the quantum-Hall effect in HOPG. This work demonstrates how powerful the combined approach between the high quality STS measurement and the first-principles calculation is in material science.
132 citations
"The electronic properties of graphe..." refers background in this paper
...faces (Kobayashi et al., 2005; Matsui et al., 2005; Niimi et al., 2006), epitaxially grown graphene stacks (Mallet et al....
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...…eld (de Gennes,1964; Nakao, 1976), and the results are also onsistentwith STM on graphite surfa es (Kobayashi et al., 2005;Li and Andrei, 2007; Matsui et al., 2005; Niimi et al.,2006), epitaxially grown graphene sta ks (Mallet et al.,2007), and with opti al measurements in the infraredrange…...
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TL;DR: In this paper, the Fermi energy dependence of the (time-averaged) current and shot noise in an impurity-free carbon bilayer (length $L⪡\text{width}$ $W$) was compared with known results for a monolayer.
Abstract: We calculate the Fermi energy dependence of the (time-averaged) current and shot noise in an impurity-free carbon bilayer (length $L⪡\text{width}$ $W$), and compare with known results for a monolayer. At the Dirac point of charge neutrality, the bilayer transmits as two independent monolayers in parallel: Both current and noise are resonant at twice the monolayer value, so that their ratio (the Fano factor) has the same $1∕3$ value as in a monolayer---and the same value as in a diffusive metal. The range of Fermi energies around the Dirac point within which this pseudodiffusive result holds is smaller, however, in a bilayer than in a monolayer (by a factor ${l}_{\ensuremath{\perp}}∕L$, with ${l}_{\ensuremath{\perp}}$ the interlayer coupling length).
130 citations
"The electronic properties of graphe..." refers background in this paper
...The conductance is, again, a summation of terms arising from evanescent waves between the two contacts, and it has the dependence on sample dimensions of a 2D conductivity of the order of e/h (Snyman and Beenakker, 2007), although there is a prefactor twice bigger than the one in single layer graphene....
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...…ondu tan e is, again, a sum-mation of terms arising from evanes ent waves betweenthe two onta ts, and it has the dependen e on sam-ple dimensions of a 2D ondu tivity of the order of e2/h(Snyman and Beenakker, 2007), although there is a pref-a tor twi e bigger than the one in single layer graphene....
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TL;DR: It is shown that, in a d-wave superconductor, the density of states, averaged over randomness, follows a nontrivial power-law behavior near the Fermi energy: $\rho(\omega) \sim |\omega|^{\alpha}$.
Abstract: We show that weak nonmagnetic impurities in a two-dimensional d-wave superconductor introduce a nontrivial exponent in the energy dependence of the single-particle density of states: \ensuremath{\rho}(\ensuremath{\omega})\ensuremath{\sim}\ensuremath{\Vert}\ensuremath{\omega}${\mathrm{\ensuremath{\Vert}}}^{\mathrm{\ensuremath{\alpha}}}$. The exponent \ensuremath{\alpha}g0 is exactly calculated for two types of disorder. We argue that the appearance of a finite \ensuremath{\rho}(0) would be equivalent to breaking of a continuous symmetry, prohibited in two dimensions. The method we use is based on the Abelian and non-Abelian bosonization of the effective model of 1D interacting fermions.
130 citations
"The electronic properties of graphe..." refers background in this paper
...The general problemof random gauge elds for Dira fermions has been exten-sively analyzed before the urrent interest in graphene,as the topi is also relevant for the IQHE (Ludwig et al.,1994) and d-wave super ondu tivity (Nersesyan et al.,1994)....
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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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TL;DR: In this article, the level broadening and transport properties of a two-dimensional system under extremely strong magnetic fields are investigated in the single-site approximation (SSA) method.
Abstract: The level broadening and transport properties of a two-dimensional system under extremely strong magnetic fields are investigated in the single-site approximation (SSA). At high concentrations of scatterers, the SSA approaches the simple damping theoretical approximation. At low concentrations, many impurity bands associated with each bound state of an isolated scatterer appear, and the nonexistence of continuous states in this system causes a singular level with zero width in case of scatterers with a δ-potential. The peak value of the conductivity of the impurity band with the angular momentum m is given by \(2\pi l^{2}N_{i}(N+m+1/2)e^{2}/\pi^{2}\hbar\), where N is the Landau quantum number and N i is the concentration of scatterers. The density of states and the conductivity are calculated explicitly for a model system which contains scatterers with the Gaussian potential.
130 citations
"The electronic properties of graphe..." refers methods in this paper
...(Ando, 1974a,b, , 1975; Ando and Uemura, 1974; Ohta,1968, 1971) using the averaging pro edure over impuritypositions of Duke (Duke, 1968)....
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TL;DR: In this article, the authors studied the electronic transmission through a graphene bilayer in the presence of an applied bias between the layers, and they considered different geometries involving interfaces between both a monolayer and a bilayer and between two bilayers.
Abstract: We study the electronic transmission through a graphene bilayer in the presence of an applied bias between the layers. We consider different geometries involving interfaces between both a monolayer and a bilayer and between two bilayers. The applied bias opens a sizable gap in the spectrum inside the bilayer barrier region, thus leading to large changes in the transmission probability and electronic conductance that are controlled by the applied bias.
128 citations
"The electronic properties of graphe..." refers background in this paper
...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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...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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...…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., 2007)....
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