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 Coulomb interaction on the scale of lattice constant was used to explain the Hall conductivity in graphene at high magnetic fields, and it was predicted that at a large in-plane component of the magnetic field such ordering may be present only at the filling factor $f=\ifmmode\pm\pm/else\textpm\fi{}1$ and absent otherwise.
Abstract: The observed quantization of the Hall conductivity in graphene at high magnetic fields is explained as being due to the dynamically generated spatial modulation of either the electron spin or the density, as decided by the details of Coulomb interaction on the scale of lattice constant. It is predicted that at a large in-plane component of the magnetic field such ordering may be present only at the filling factor $f=\ifmmode\pm\else\textpm\fi{}1$ and absent otherwise. Other experimental consequences of the theory are outlined.
106 citations
Additional excerpts
...Therefore, the Hall on-du tivity is (Gusynin and Sharapov, 2005; Herbut, 2007;Peres et al., 2006 ,d; S hakel, 1991): σxy = I VH = c VH δE δΦ = ±2(2N + 1)e 2 h , (111)without any Hall plateau at N = 0....
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TL;DR: It is proposed that the inversion symmetry of the graphene honeycomb lattice is spontaneously broken via a magnetic-field-dependent Peierls distortion, which leads to valley splitting of the n=0 Landau level but not of the other Landau levels.
Abstract: We propose that the inversion symmetry of the graphene honeycomb lattice is spontaneously broken via a magnetic-field-dependent Peierls distortion. This leads to valley splitting of the n=0 Landau level but not of the other Landau levels. Compared to Quantum Hall valley ferromagnetism recently discussed in the literature, lattice distortion provides an alternative explanation to all of the currently observed Quantum Hall plateaus in graphene.
105 citations
TL;DR: In this paper, the spin-orbit interaction lifted all band degeneracies (other than the Kramers degeneracy), and affects the graphite Fermi-surface topology at the Brillouin-zone boundary.
Abstract: Using symmetry arguments, the effective-mass Hamiltonian including spin-orbit interaction is derived for energy bands with extrema near the vertical edge of the hexagonal prism which represents the Brillouin zone of graphite. The energy bands in the plane normal to the vertical edge are described by k\ifmmode\cdot\else\textperiodcentered\fi{}p perturbation theory, whereas along the edge a Fourier expansion is used for all the matrix elements. It is shown that spin-orbit interaction lifts all band degeneracies (other than the Kramers degeneracy), and affects the graphite Fermi-surface topology at the Brillouin-zone boundary ${k}_{z}=\ifmmode\pm\else\textpm\fi{}\frac{\ensuremath{\pi}}{{c}_{0}}$, where two de Haas-van Alphen periods are predicted. Magnetic energy levels for a static magnetic field H\ensuremath{\parallel}c are obtained by solution of the effective-mass Hamiltonian. Selection rules for infrared interband transitions are discussed. An evaluation of the spin-orbit band parameters is suggested by analysis of structure in the low-quantum-limit magneto-reflection data and of the low-frequency de Haas-van Alphen oscillations.
104 citations
"The electronic properties of graphe..." refers background in this paper
...The intrin-si and extrinsi spin orbit intera tions an be writtenas (Dresselhaus and Dresselhaus, 1965; Kane and Mele,2005): HSO;int ≡ ∆so ∫ d2rΨ̂†(r)ŝz σ̂z τ̂zΨ̂(r) , HSO;ext ≡ λR ∫ d2rΨ̂†(r)(−ŝxσ̂y+ŝyσ̂xτ̂z)Ψ̂(r) ,(124)where σ̂ and τ̂ are Pauli matri es whi h des ribe the sub-latti e and valley…...
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...The spin orbit intera tion leads to a spin de-pendent shift of the orbitals, whi h is of a di erent signfor the two sublatti es, a ting as an e e tive mass withinea h Dira point (Dresselhaus and Dresselhaus, 1965;Kane and Mele, 2005; Wang and Chakraborty, 2007a)....
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TL;DR: It is shown that the eigenstates of the problem can be cast in terms of coherent states, which appears in a natural way from the formalism.
Abstract: We present an exact algebraic solution of a single graphene plane in transverse electric and perpendicular magnetic fields. The method presented gives both the eigenvalues and the eigenfunctions of the graphene plane. It is shown that the eigenstates of the problem can be cast in terms of coherent states, which appears in a natural way from the formalism.
103 citations
Additional excerpts
...See: (Lukose et al., 2007; Peres and Castro,2007)....
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TL;DR: The mechanism of delocalization of two-dimensional Dirac fermions with random mass was investigated in this paper, using a superfield representation, where one fermion component can delocalize due to the spontaneous breaking of a special supersymmetry of the model.
Abstract: The mechanism of delocalization of two-dimensional Dirac fermions with random mass is investigated, using a superfield representation. Although localization effects are very strong, one fermion component can delocalize due to the spontaneous breaking of a special supersymmetry of the model. The delocalized fermion has a nonsingular density of states and is described by a diffusion propagator. Supersymmetry is restored if the mean of the random mass is sufficiently large. This is accompanied by a critical boson component.
102 citations
"The electronic properties of graphe..." refers background in this paper
...which is the so-called universal conductivity of graphene (Fradkin, 1986a,b; Katsnelson, 2006b; Lee, 1993; Ludwig et al., 1994; Peres et al., 2006c; Tworzyd lo et al., 2006; Yang and Nayak, 2002; Ziegler, 1998)....
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...(203)and (204) redu e to: σ0 = 4 π e2 h , (205)whi h is the so- alled universal ondu tivity of graphene(Fradkin, 1986a,b; Katsnelson, 2006b; Lee, 1993;Ludwig et al., 1994; Nersesyan et al., 1994; Peres et al.,2006 ; Tworzydlo et al., 2006; Yang and Nayak, 2002;Ziegler, 1998)....
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