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: In this paper, the boundary condition for the Dirac equation corresponding to a tight-binding model on a two-dimensional honeycomb lattice terminated along an arbitrary direction was derived.
Abstract: We derive the boundary condition for the Dirac equation corresponding to a tight-binding model on a two-dimensional honeycomb lattice terminated along an arbitrary direction Zigzag boundary conditions result generically once the boundary is not parallel to the bonds Since a honeycomb strip with zigzag edges is gapless, this implies that confinement by lattice termination does not, in general, produce an insulating nanoribbon We consider the opening of a gap in a graphene nanoribbon by a staggered potential at the edge and derive the corresponding boundary condition for the Dirac equation We analyze the edge states in a nanoribbon for arbitrary boundary conditions and identify a class of propagating edge states that complement the known localized edge states at a zigzag boundary
409 citations
TL;DR: In this paper, the first direct observation of relativistic Dirac fermions with linear dispersion near the Brillouin zone (BZ) corner H was reported.
Abstract: Originating from relativistic quantum field theory, Dirac fermions have been invoked recently to explain various peculiar phenomena in condensed-matter physics, including the novel quantum Hall effect in graphene1,2, the magnetic-field-driven metal–insulator-like transition in graphite3,4, superfluidity in 3He (ref. 5) and the exotic pseudogap phase of high-temperature superconductors6,7. Despite their proposed key role in those systems, direct experimental evidence of Dirac fermions has been limited. Here, we report the first direct observation of relativistic Dirac fermions with linear dispersion near the Brillouin zone (BZ) corner H, which coexist with quasiparticles that have a parabolic dispersion near another BZ corner K. In addition, we also report a large electron pocket that we attribute to defect-induced localized states. Thus, graphite presents a system in which massless Dirac fermions, quasiparticles with finite effective mass and defect states all contribute to the low-energy electronic dynamics.
405 citations
TL;DR: The weak-localization correction to the conductivity for disordered electrons in a two-dimensional honeycomb lattice is calculated and it can be either positive or negative depending on the interaction range of impurity potentials.
Abstract: We have calculated the weak-localization correction to the conductivity for disordered electrons in a two-dimensional honeycomb lattice and shown that it can be either positive or negative depending on the interaction range of impurity potentials. From symmetry considerations, the symplectic class turns out to be realized at nonzero temperatures and crossover to the orthogonal class is predicted with decreasing temperature.
393 citations
"The electronic properties of graphe..." refers background in this paper
...Hen e, elasti strains that modify therelative orientation of the atoms also lead to an e e tivegauge eld, whi h a ts on ea h K point separately, as rst dis ussed in relation to arbon nanotubes (Mañes,2007; Suzuura and Ando, 2002b)....
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...As a onsequen e, the two paths inter-fere destru tively, leading to a suppression of ba ks atter-ing (Suzuura and Ando, 2002a)....
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TL;DR: In graphene, the phonon anharmonic lifetimes and decay channels of the A(1)' mode at K dominate over E(2g) at Gamma and couple strongly with acoustic phonons, highlighting how ballistic transport in carbon-based interconnects requires careful engineering of phonon decays and thermalization.
Abstract: We determine from first principles the finite-temperature properties-linewidths, line shifts, and lifetimes-of the key vibrational modes that dominate inelastic losses in graphitic materials. In graphite, the phonon linewidth of the Raman-active E(2g) mode is found to decrease with temperature; such anomalous behavior is driven entirely by electron-phonon interactions, and does not appear in the nearly degenerate infrared-active E(1u) mode. In graphene, the phonon anharmonic lifetimes and decay channels of the A(1)' mode at K dominate over E(2g) at Gamma and couple strongly with acoustic phonons, highlighting how ballistic transport in carbon-based interconnects requires careful engineering of phonon decays and thermalization.
389 citations
"The electronic properties of graphe..." refers background in this paper
...Non-linear effects such as large bending deformations (Peliti and Leibler, 1985), the coupling between flexural and in-plane modes (or phonon-phonon interactions (Bonini et al., 2007)) and the presence of topological defects (Nelson, D....
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...…e e ts su h as large bending deformations (Peliti and Leibler,1985), the oupling between exural and in-plane modes(or phonon-phonon intera tions (Bonini et al., 2007;Radzihovsky and Le Doussal, 1992)) and the presen eof topologi al defe ts (Nelson and Peliti, 1987) an leadto strong…...
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TL;DR: It is shown how the shape and quality of graphene flakes affect the values of the elastic and inelastic rates and their physical origin, and the characteristic rates that determine it are found.
Abstract: We show that the manifestation of quantum interference in graphene is very different from that in conventional two-dimensional systems. Because of the chiral nature of charge carriers, it is not only sensitive to inelastic, phase-breaking scattering, but also to a number of elastic scattering processes. We study weak localization in different samples and at different carrier densities, including the Dirac region, and find the characteristic rates that determine it. We show how the shape and quality of graphene flakes affect the values of the elastic and inelastic rates and discuss their physical origin.
389 citations
"The electronic properties of graphe..." refers background in this paper
...tally, localization effects are always strongly suppressed close to the Dirac point but can be partially or, in rare cases, completely recovered at high carrier concentrations, depending on a particular single-layer sample (Morozov et al., 2006; Tikhonenko et al., 2008)....
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