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, an n-m combination rule is proposed to classify graphene cones by the localized fictitious apical flux through their apices, leading to two classes of graphene cones with two apical pentagons.
Abstract: Multiple five- and seven-membered rings in graphene surfaces have long-range effects which are very sensitive to their relative placement. The sensitivity is described by an "n-m" combination rule derived here. This rule classifies graphene cones by the localized fictitious gauge flux through their apices, leading to two classes of graphene cones with two apical pentagons. The local density of states vanishes at the Fermi energy in one class, but in the other, it is nonzero and decreases inversely with distance from the apex. Fictitious apical flux also affects the response of electrons to a magnetic field, leading to position dependent local degeneracy of Landau levels as well as anomalous Landau levels which are semiclassically linked to cyclotron orbits which encircle the apex multiple times before closing. We derive these results in a continuum theory, but confront them with numerical tight-binding computations, finding good agreement. We also discuss an intrinsic Aharonov-Bohm effect which persists in the ray-optics limit, and possibilities for producing different inhomogeneous effective fields by exploiting the conical shape.
123 citations
"The electronic properties of graphe..." refers background in this paper
...The nal ontinuum equation gives a reasonable des rip-tion of the ele troni spe trum of fullerenes of di er-ent sizes (González et al., 1992, 1993b), and other stru -tures whi h ontain pentagons (Kolesnikov and Osipov,2004, 2006; Lammert and Crespi, 2004; LeClair, 2000;Osipov et al., 2003)....
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TL;DR: A realization of QED{sub 2+1} at finite density in the context of (planar) gapless semiconductors is suggested.
Abstract: Quantum electrodynamics in 2+1 dimensions (${\mathrm{QED}}_{2+1}$) at finite density and temperature is analyzed by reducing it to an effective (0+1)-dimensional theory. A realization of ${\mathrm{QED}}_{2+1}$ at finite density in the context of (planar) gapless semiconductors is suggested.
122 citations
TL;DR: It is shown that zero-energy edge states in bilayer graphene can be divided into two families: (i) states living only on a single plane, equivalent to surface states in monolayer graphene and (ii) states with a finite amplitude over the two layers, with an enhanced penetration into the bulk.
Abstract: We report the existence of zero-energy surface states localized at zigzag edges of bilayer graphene. Working within the tight-binding approximation we derive the analytic solution for the wave functions of these peculiar surface states. It is shown that zero-energy edge states in bilayer graphene can be divided into two families: (i) states living only on a single plane, equivalent to surface states in monolayer graphene and (ii) states with a finite amplitude over the two layers, with an enhanced penetration into the bulk. The bulk and surface (edge) electronic structure of bilayer graphene nanoribbons is also studied, both in the absence and in the presence of a bias voltage between planes.
122 citations
Book•
01 Jan 2005
TL;DR: In this article, the authors describe the structure of Condensed matter: symmetry of structure, Symmetry of Structure, Organization of Crystalline State, Beyond the Crystallized State, Inhomogeneous Structures and Wave Behavior in Various Structures.
Abstract: # Structure of Condensed Matter: # Symmetry of Structure # Organization of the Crystalline State # Beyond the Crystalline State # Inhomogeneous Structures # Wave Behavior in Various Structures: # Wave Propagation in Periodic and Quasiperiodic Structures # Dynamics of Bloch Electrons # Surface and Impurity Effects # Transport Properties # Wave Localization in Disordered Structures # Mesoscopic Quantum Transport # Bonds, Bands with Things Between and Beyond: # Bond Approach # Band Approach # Correlated Electronic States # Quantum Confined Nanostructures # Broken Symmetry and Ordered Phases: # Landau Theory of Phase Transitions # Crystals, Quasicrystals and Liquid Crystals # Ferromagnets, Antiferromagnets and Ferrimagnets # Superconductors and Superfluids # Broken Ergodicity
122 citations
"The electronic properties of graphe..." refers background in this paper
...This is noth-ing but the rumpling instability of soft membranes(Chaikin and Lubensky, 1995; Nelson et al., 2004)....
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...It is instru tive to understand how thesemodes appear from the point of view of elasti ity the-ory (Chaikin and Lubensky, 1995; Nelson et al., 2004)....
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...…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 renormalizations of the bending rigidity, driv-ing the system toward a at phase at low tempera-tures (Chaikin and Lubensky, 1995)....
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TL;DR: The band structure of graphite with the hypothetical simple hexagonal structure has been investigated near the Fermi energy, using a tight-binding approximation, and possible application to disordered graphite (turbostratic).
Abstract: The band structure of graphite with the hypothetical simple hexagonal structure has been investigated near the Fermi energy, using a tight-binding approximation. Some general features of the structure of the π bands in the neighborhood of the zone edge are obtained and are expressed in terms of appropriate parameters. The Fermi surface is analyzed. The density of states and the resulting behavior near the Fermi level are compared to the results obtained for the Bernal structure (Slonczewski-Weiss-McClure model) and for the rhombohedral structure (Haering-McClure model). Possible application to disordered graphite (turbostratic) is also discussed.
119 citations
"The electronic properties of graphe..." refers background in this paper
...…in nature, although a sta k-ing order in whi h all atoms in one layer o upy posi-tions dire tly above the atoms in the neighboring layers(hexagonal sta king) has been onsidered theoreti ally(Charlier et al., 1991) and appears in graphite inter a-lated ompounds (Dresselhaus and Dresselhaus, 2002)....
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