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
References
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Book•
01 Jan 1969
TL;DR: In this paper, the authors present an extension of the Dirac Equation to the Relavistic Spin 1/2 Particle Equation (RS-1/2): Klein-Gordon Equation.
Abstract: * Photon Polarization * Neutral K Mesons * The Motion of Particles in Quantum Mechanics * Potential Problems, Mostly in One Dimension * Equations of Motion for Operators * Orbital Angular Momentum and Central Potentials * The Hydrogen Atom * Cooper Pairs * Potential Scattering * Coulomb Scattering * Stationary State Perturbation Theory * Time-Dependent Perturbation Theory * Interaction of Radiation with Matter * Spin 1/2 * Addition of Angular Momenta * Isotopic Spin * Rotations and Tensor Operators * Identical Particles * Second Quantization * Atoms * Molecules * Relavistic Spin Zero Particles: Klein-Gordon Equation * Relavistic Spin 1/2 Particles: Dirac Equation
574 citations
"The electronic properties of graphe..." refers background in this paper
...Its solutionhas many of the features of the 3D relativisti hydro-gen atom problem (Baym, 1969)....
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TL;DR: Graphene is the first example of truly two-dimensional crystals as mentioned in this paper, and it is a gapless semiconductor with unique electronic properties resulting from the fact that charge carriers in graphene demonstrate charge-conjugation symmetry between electrons and holes and possess an internal degree of freedom similar to "chirality" for ultrarelativistic elementary particles.
564 citations
"The electronic properties of graphe..." refers background in this paper
...…by the fa t thatin graphene the Dira fermions move with a speed vFwhi h is 300 times smaller than the speed of light, c. Hen e, many of the unusual properties of QED an show up in graphene but at mu h smaller speeds(Castro Neto et al., 2006a; Katsnelson and Novoselov,2007; Katsnelson et al., 2006)....
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TL;DR: In this paper, the de Haas-van Alphen effect in the magnetic susceptibility of graphite has been interpreted by applying the susceptibility formula for general bands of Lifschitz and Kosevich to the band model of Slonczewski.
Abstract: The de Haas-van Alphen effect in the magnetic susceptibility of graphite has been interpreted by applying the susceptibility formula for general bands of Lifschitz and Kosevich to the band model of Slonczewski. The majority electrons and holes are responsible for the two periods of oscillation of the susceptibility. The analysis yields information concerning the band structure: (1) the total band overlap is about 0.03 ev, (2) the energy difference between the two doubly degenerate bands at the corner of the Brillouin zone is about 0.025 ev, (3) ${\ensuremath{\gamma}}_{0}$ must be larger than about 1.2 ev, and (4) the relation ${\ensuremath{\gamma}}_{1}=0.04{{\ensuremath{\gamma}}_{0}}^{2}$ holes approximately (where both $\ensuremath{\gamma}'\mathrm{s}$ are in ev and correspond to Wallace's notation). Calculated carrier densities are 2.4\ifmmode\times\else\texttimes\fi{}${10}^{\ensuremath{-}5}$ per atom for electrons and 1.8\ifmmode\times\else\texttimes\fi{}${10}^{\ensuremath{-}5}$ per atom for holes, in rough agreement with estimates made from galvanomagnetic data. Rough agreement with electron specific-heat data is also obtained.
560 citations
"The electronic properties of graphe..." refers background or methods in this paper
..., 2004) confirm the main features of this model, formulated mainly on the basis of Fermi surface measurements (McClure, 1957; Soule et al., 1964)....
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...The values of these parameters, and their dependence with pressure, or, equivalently, the interatomic distances, have been extensively studied (Dillon et al., 1977; Dresselhaus and Mavroides, 1964; McClure, 1957; Nozières, 1958; Soule et al., 1964)....
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...Weiss-McClure (SWM) band structure of graphite which provided a detailed description of the electronic properties in this material (McClure, 1957; Slonczewski and Weiss, 1958) and was very successful in describing the experimental data (Boyle and Nozières, 1958; Dillon et al....
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TL;DR: In this article, the electronic structure and Landau levels of multi-layer GAs with different stacking orders were analyzed, and it was shown that electrostatic effects can induce a strongly divergent density of states in bi-and tri-layers, reminiscent of one-dimensional systems.
Abstract: We analyze, within a minimal model that allows analytical calculations, the electronic structure and Landau levels of graphene multi-layers with different stacking orders. We find, among other results, that electrostatic effects can induce a strongly divergent density of states in bi- and tri-layers, reminiscent of one-dimensional systems. The density of states at the surface of semi-infinite stacks, on the other hand, may vanish at low energies, or show a band of surface states, depending on the stacking order.
554 citations
"The electronic properties of graphe..." refers background in this paper
...Simple analytical expressions for the electronic bands can be obtained for perfect Bernal ( 1212 · · · ) and rhombohedral ( 123123 · · · ) stacking (Guinea et al., 2006)....
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...In an in nite rhombohedral sta k, the Landau lev-els remain dis rete and quasi-2D (Guinea et al., 2006)....
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...In sta ks with rhombohedral sta k- ing, all sites have one neighbor in another plane, andthe density of states vanishes at ǫ = 0 (Guinea et al.,2006)....
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...Simple analyti al expressions for theele troni bands an be obtained for perfe t Bernal ( 1212 · · · ) and rhombohedral ( 123123 · · · ) sta king(Guinea et al., 2006)....
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...the density of states vanishes at = 0 (Guinea et al., 2006)....
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TL;DR: In this paper, the authors reviewed the recent progress of the experimental studies on ultra-thin films of graphite and hexagonal boron nitride (h-BN) by using angle-resolved electron spectroscopy together with other techniques.
Abstract: In this article, we have reviewed the recent progress of the experimental studies on ultra-thin films of graphite and hexagonal boron nitride (h-BN) by using angle-resolved electron spectroscopy together with other techniques. The fundamental properties of these high-quality films are discussed on the basis of the data on dispersion relations of valence electrons, phonon dispersion etc. The interfacial orbital mixing of the -state of the monolayer graphite (MG) with the d states of the reactive substrates is the origin for the phonon softening, expansion of the nearest-neighbour C - C distance, modification of the -band, low work function, and two-dimensional plasmons with high electron density, etc. In the cases of weak mixing at the interface between the MG and relatively inert substrates, the observed properties of the MG are very close to the bulk ones. In contrast to the case for MG, the interfacial interaction between the h-BN monolayer and the substrate is weak.
553 citations