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 authors analyzed the electronic properties of Aharonov-Bohm rings made of graphene and showed that the combined effect of the ring confinement and applied magnetic flux offers a controllable way to lift the orbital degeneracy originating from the two valleys, even in the absence of intervalley scattering.
Abstract: We analyze theoretically the electronic properties of Aharonov-Bohm rings made of graphene. We show that the combined effect of the ring confinement and applied magnetic flux offers a controllable way to lift the orbital degeneracy originating from the two valleys, even in the absence of intervalley scattering. The phenomenon has observable consequences on the persistent current circulating around the closed graphene ring, as well as on the ring conductance. We explicitly confirm this prediction analytically for a circular ring with a smooth boundary modeled by a space-dependent mass term in the Dirac equation. This model describes rings with zero or weak intervalley scattering so that the valley isospin is a good quantum number. The tunable breaking of the valley degeneracy by the flux allows for the controlled manipulation of valley isospins. We compare our analytical model to another type of ring with strong intervalley scattering. For the latter case, we study a ring of hexagonal form with lattice-terminated zigzag edges numerically. We find for the hexagonal ring that the orbital degeneracy can still be controlled via the flux, similar to the ring with the mass confinement.
200 citations
TL;DR: In this article, the elastic scattering theory for the two-dimensional massive Dirac fermions in the presence of an axially symmetric potential has been thoroughly outlined and applied to scattering off a smooth short-ranged potential.
Abstract: Electron properties of graphene are described in terms of Dirac fermions. Here we thoroughly outline the elastic scattering theory for the two-dimensional massive Dirac fermions in the presence of an axially symmetric potential. While the massless limit is relevant for pristine graphene, keeping finite mass allows for generalizations onto situations with broken symmetry between the two sublattices and provides a link to the scattering theory of electrons in a parabolic band. We demonstrate that the Dirac theory requires short-distance regularization for potentials which are more singular than $1∕r$. The formalism is then applied to scattering off a smooth short-ranged potential. Next, we consider the Coulomb potential scattering, where the Dirac theory is consistent for a point scatterer only for the effective impurity strength below $1∕2$. From the scattering phase shifts we obtain the exact Coulomb transport cross section in terms of the impurity strength. The results are relevant for transport in graphene in the presence of impurities that do not induce scattering between the Dirac points in the Brillouin zone.
198 citations
"The electronic properties of graphe..." refers background or methods or result in this paper
...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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...…based on s reened harged impurities it ispossible to obtain from a Boltzmann equation ap-proa h a ondu tivity varying linearly with the den-sity, in agreement with the experimental result (Ando,2006b; Katsnelson and Geim, 2008; Novikov, 2007b;Peres et al., 2007b; Trushin and S hliemann, 2007)....
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...Passivation an be modeled in thetight-binding approa h by modi ations of the hoppingenergies (Novikov, 2007 ) or via additional phases in theboundary onditions (Kane and Mele, 1997)....
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TL;DR: The beta function of a two-dimensional massless Dirac Hamiltonian subject to a random scalar potential, which, e.g., underlies theoretical descriptions of graphene, is computed numerically and provides an argument based on the spectral flows under twisting boundary conditions, which shows that none of the states of the masslessDirac Hamiltonians can be localized.
Abstract: The beta function of a two-dimensional massless Dirac Hamiltonian subject to a random scalar potential, which, e.g., underlies theoretical descriptions of graphene, is computed numerically. Although it belongs to, from a symmetry standpoint, the two-dimensional symplectic class, the beta function monotonically increases with decreasing conductance. We also provide an argument based on the spectral flows under twisting boundary conditions, which shows that none of the states of the massless Dirac Hamiltonian can be localized.
196 citations
"The electronic properties of graphe..." refers background in this paper
...…of intera ting ele -trons in a random gauge eld suggests the possibilityof non-trivial phases (Aleiner and Efetov, 2006; Altland, 2006; Dell'Anna, 2006; Foster and Ludwig, 2006a,b;Khvesh henko, 2007; Nomura et al., 2007; Stauber et al.,2005), where intera tions and disorder an el ea h other....
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...The interband exchange energy is reduced in a bilayer (Nomura et al., 2007), and a positive contribution that depends logarithmically on the bandwidth in graphene is absent in its bilayer....
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...In fa t, analyti al and numeri alstudies (Bardarson et al., 2007; Lewenkopf et al., 2007;Nomura et al., 2007; San-Jose et al., 2007) show that the ondu tivity obeys a universal s aling with the latti esize L: σ(L) = 2e2 h (A ln(L/ξ) +B) , (180)where ξ is a length s ale asso iated with range of…...
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...Higher order corrections to (227) lead to a first order transition at slightly higher densities (Nomura et al., 2007)....
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...…e ts that a e t the strength and rangeof the Coulomb intera tion, are rather non-trivial ingraphene (Fogler et al., 2007b; Shklovskii, 2007) and,therefore, important for the interpretation of transportdata (Bardarson et al., 2007; Lewenkopf et al., 2007;Nomura et al., 2007; San-Jose et al., 2007)....
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TL;DR: In this paper, the effects of symmetry breaking in 4-fermion models in 2 + 1 dimensions were quantitatively studied using the 1/N expansion and showed that these models are renormalizable in this framework, in spite of their non-renormalizability in weak coupling expansion.
195 citations
"The electronic properties of graphe..." refers background in this paper
...This result re-mains true even to higher order in perturbation theory(Mish henko, 2007) and is also obtained in large N ex-pansions (Rosenstein et al., 1989, 1991; Son, 2007) (N isthe number of avors of Dira fermions), with the onlymodi ation being the prefa tor in (220)....
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TL;DR: A polarized Raman study of nanographite ribbons on a highly oriented pyrolytic graphite substrate is reported, which shows the Raman peak of the nanographites exhibits an intensity dependence on the light polarization direction relative to the nanographsite ribbon axis.
Abstract: A polarized Raman study of nanographite ribbons on a highly oriented pyrolytic graphite substrate is reported The Raman peak of the nanographite ribbons exhibits an intensity dependence on the light polarization direction relative to the nanographite ribbon axis This result is due to the quantum confinement of the electrons in the 1D band structure of the nanographite ribbons, combined with the anisotropy of the light absorption in 2D graphite, in agreement with theoretical predictions
194 citations