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 article, the authors considered a model of weak disorder that corresponds to an armchair ribbon whose width randomly changes by a single unit cell size, and found that the low-temperature conductivity is governed by an effective one-dimensional hopping between segments of distinct band structure.
Abstract: We study electronic transport in graphene nanoribbons with rough edges. We first consider a model of weak disorder that corresponds to an armchair ribbon whose width randomly changes by a single unit cell size. We find that in this case, the low-temperature conductivity is governed by an effective one-dimensional hopping between segments of distinct band structure. We then provide numerical evidence and qualitative arguments that similar behavior also occurs in the limit of strong uncorrelated boundary disorder.
84 citations
TL;DR: The energy band structure of graphite is described in the region of the Fermi surfaces by the Slonczewski-Weiss model and it is yet clear if the correlation of electron motion due to the coulomb interaction causes important discrepancies between the predictions of the model and the experimental results.
Abstract: The energy band structure of graphite is described in the region of the Fermi surfaces by the Slonczewski-Weiss model. The electron and hole Fermi surfaces are highly elongated and are aligned along the six Brillouin zone edges which are parallel to the trigonal axis of the crystal. The energy is a nonparabolic function of wavenumber and the Fermi surfaces are not ellipsoids. Galvanomagnetic, de Haasvan Alphen, and other experiments have established that: the band overlap is about 0.03 to 0.04 eV, the carrier densities of electrons and holes are each about 3 × 1018 cm-3 at low temperatures, the effective masses perpendicular to the trigonal axis are about 0.04 m0 for electrons and 0.06 m0 for holes, and the length-to-width ratio of the Fermi surfaces is about 12. The only important effect not included in the Slonczewski-Weiss model is the correlation of electron motion due to the coulomb interaction. Though this effect is expected to be important a priori, it is not yet clear if it causes important discrepancies between the predictions of the model and the experimental results.
82 citations
77 citations
"The electronic properties of graphe..." refers background in this paper
...For t′ = 0 it is possible to derivean analyti al expression for the density of states per unit ell, whi h has the form (Hobson and Nierenberg, 1953): ρ(E) = 4 π2 |E| t2 1√ Z0 F ( π 2 , √ Z1 Z0 ) Z0 =...
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...For t′ = 0 it is possible to derive an analytical expression for the density of states per unit cell, which has the form (Hobson and Nierenberg, 1953):...
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TL;DR: The TR-PES investigation of the energy dependence of the electron relaxation lifetime in highly oriented pyrolytic graphite provides the first experimental evidence that the dominant scattering process in layered materials can be electronplasmon scattering, even for excitations close to the Fermi level.
Abstract: We comment on the theoretical interpretations applied to a recent experiment on electron lifetime in graphite. We point out that the acoustic-plasmon excitations in a layered two-dimensional electron system do not produce a linear energy dependence for the Coulomb scattering rate.
76 citations
"The electronic properties of graphe..." refers background in this paper
...larger with respect to the interlayer interactions (Sugawara et al., 2007; Xu et al., 1996)....
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...The linear depen-den e of the inverse quasiparti le lifetime with energy is onsistent with photo-emission experiments in graphite,for energies larger with respe t to the interlayer inter-a tions (Bostwi k et al., 2007b; Sugawara et al., 2007;Xu et al., 1996; Zhou et al., 2006a, )....
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TL;DR: In this paper, the authors propose the theory of transport in a gate-tunable graphene junction, in which the gradient of the carrier density is controlled by the gate voltage, and find the conditions for observing ballistic transport and show that in existing devices they are satisfied only marginally.
Abstract: We propose the theory of transport in a gate-tunable graphene $p\text{\ensuremath{-}}n$ junction, in which the gradient of the carrier density is controlled by the gate voltage. Depending on this gradient and on the density of charged impurities, the junction resistance is dominated by either diffusive or ballistic contribution. We find the conditions for observing ballistic transport and show that in existing devices they are satisfied only marginally. We also simulate numerically the trajectories of charge carriers and illustrate challenges in realizing more delicate ballistic effects, such as Veselago lensing.
76 citations