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: The theoretical results, strikingly different from the standard 2D electron gas, are explained using a "Lorentz boost," and as an "instability of a relativistic quantum field vacuum."
Abstract: A new effect in graphene in the presence of crossed uniform electric and magnetic fields is predicted. Landau levels are shown to be modified in an unexpected fashion by the electric field, leading to a collapse of the spectrum, when the value of electric to magnetic field ratio exceeds a certain critical value. Our theoretical results, strikingly different from the standard 2D electron gas, are explained using a "Lorentz boost," and as an "instability of a relativistic quantum field vacuum." It is a remarkable case of emergent relativistic type phenomena in nonrelativistic graphene. We also discuss few possible experimental consequence.
238 citations
Additional excerpts
...See: (Lukose et al., 2007; Peres and Castro,2007)....
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...See: (Lukose et al., 2007)....
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TL;DR: The agreement suggests that the dielectric function of stage-1, acceptor-type graphite intercalated compounds (GIC's) is reliable in describing the dynamic screening mechanism for GIC's.
Abstract: In this paper, we carefully study the dielectric function of stage-1, acceptor-type graphite intercalated compounds (GIC's). We model the system by a superlattice of an infinite number of graphite layers, each of which has the band structure described by the two-dimensional calculation of Blinowski et al. Tunneling between graphite layers is neglected, and so are effects due to intercalants except that of determining the Fermi level. However, we have retained a Coulomb term that describes the interaction between electrons on different layers. With this model, we are able to express the result in analytical form, and our treatment is essentially exact. Because of the Coulomb interaction along the c axis, the excitation spectrum has a plasmon band in the (q,\ensuremath{\omega}) plane, where q is the in-plane momentum transfer and \ensuremath{\omega} the energy transfer. This plasmon band is typical for the superlattice structure and contains a three-dimensional mode. We find that, despite the presence of a complicated band structure in GIC's, the three-dimensional characteristics of the plasmons still dominate. A quantitative comparison of plasmon structure between our theory and electron scattering experiments is made in this work. We obtain reasonable agreements between our theory and the measurement, concerning the plasmon energy, the plasmon width, and the plasmon intensity. The agreement suggests that our dielectric function is reliable in describing the dynamic screening mechanism for GIC's.
235 citations
"The electronic properties of graphe..." refers background in this paper
...This polarization fun tion has been also al ulated in the presen e of a nite hemi al poten-tial (Ando, 2006b; Hwang and Das Sarma, 2007; Shung,1986a,b; Wuns h et al., 2006)....
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...Campagnoli, G., and E. Tosatti, 1989, in Progress on Ele tronProperties of Metals, edited by R. Girlanda et al (KluwerA ademi Publishing), p. 337.Can ado, L. G., M. A. Pimenta, R. B. R. Neves, G. Medeiros-Ribeiro, T. Enoki, Y. Kobayashi, K. Takai, K.-I. Fukui,M. S. Dresselhaus, R. Saito, and A. Jorio, 2004, Phys....
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...A ordingly, there are olle tive plasma inter-a tions near q → 0, whi h disperse as ωp ∼ √|q|, sin ethe system is 2D (Campagnoli and Tosatti, 1989; Shung,1986a,b)....
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...Besides that,the 2DEG an also sustain olle tive ex itations su h asplasmons that have dispersion: ωplasmon(q) ∝ √q, andexist outside the ele tron-hole ontinuum at su ientlylong wavelengths (Shung, 1986a)....
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...In the random phase approxima-tion (RPA), the polarization fun tion an be al ulatedanalyti ally (González et al., 1993a, 1994; Shung, 1986a): Π(q, ω) = q2 4 √ v2F q 2 − ω2 , (215)and hen e, for ω > vF q the polarization fun tion is imag-inary indi ating the damping of ele tron-hole pairs....
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TL;DR: In this article, the transport properties of a bilayer graphene were studied theoretically within a self-consistent Born approximation, and it was shown that the conductivity of the bilayer can reach a value of 2.2π √ √ σ 2 σ σ −1 −2 σ−1 per spin in the strong disorder regime, independent of the short or long-range disorder.
Abstract: The transport properties of a bilayer graphene are studied theoretically within a self-consistent Born approximation. The electronic spectrum is composed of $k$-linear dispersion in the low-energy region and $k$-square dispersion as in an ordinary two-dimensional metal at high energy, leading to a crossover between different behaviors in the conductivity on changing the Fermi energy or disorder strengths. We find that the conductivity approaches $2{e}^{2}∕{\ensuremath{\pi}}^{2}\ensuremath{\hbar}$ per spin in the strong-disorder regime, independently of the short- or long-range disorder.
233 citations
"The electronic properties of graphe..." refers background in this paper
...Moreover, this orresponden e remains valid for the ase of a bilayer without and with trigonal warping e e ts(Cserti et al., 2007a; Koshino and Ando, 2006)....
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TL;DR: Screening of charge impurities in graphene is analyzed using the exact solution for vacuum polarization obtained from the massless Dirac-Kepler problem, showing the polarization distribution is shown to have a power law profile, leading to screening of the excess charge at large distances.
Abstract: Screening of charge impurities in graphene is analyzed using the exact solution for vacuum polarization obtained from the massless Dirac-Kepler problem. For the impurity charge below a certain critical value, no density perturbation is found away from the impurity, in agreement with perturbation theory. For the supercritical charge, however, the polarization distribution is shown to have a power law profile, leading to screening of the excess charge at large distances. The Dirac-Kepler scattering states give rise to standing wave oscillations in the local density of states which are prominent in the supercritical regime.
232 citations
"The electronic properties of graphe..." refers methods in this paper
...The solution of the Dirac equation for the Coulomb potential in 2D can be studied analytically (Biswas et al., 2007; DiVincenzo and Mele, 1984; Novikov, 2007b; Pereira et al., 2007; Shytov et al., 2007)....
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...Thesolution of the Dira equation for the Coulomb poten-tial in 2D an be studied analyti ally (Biswas et al.,2007; DiVin enzo and Mele, 1984; Novikov, 2007a;Pereira et al., 2007b; Shytov et al., 2007)....
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TL;DR: In this paper, the authors address the problem of an unscreened Coulomb charge in graphene and calculate the local density of states and displaced charge as a function of energy and distance from the impurity.
Abstract: We address the problem of an unscreened Coulomb charge in graphene and calculate the local density of states and displaced charge as a function of energy and distance from the impurity. This is done nonperturbatively in two different ways: (1) solving the problem exactly by studying numerically the tight-binding model on the lattice and (2) using the continuum description in terms of the 2D Dirac equation. We show that the Dirac equation, when properly regularized, provides a qualitative and quantitative low energy description of the problem. The lattice solution shows extra features that cannot be described by the Dirac equation: namely, bound state formation and strong renormalization of the van Hove singularities.
232 citations