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 diamagnetism of graphite including the effects of trigonal warping of the Fermi surfaces has been performed using Fukuyama's formulation of the diamagnetic properties of Bloch electrons.
Abstract: A calculation of the diamagnetism of graphite including the effects of trigonal warping of the Fermi surfaces has been performed using Fukuyama's formulation of the diamagnetism of Bloch electrons. Inclusion of the trigonal warping increases the diamagnetism by about 13% at low temperatures and reduces it by about 1% at high temperatures. A paramagnetic constant is used to represent all effects not associated with the free carriers. The experimental diamagnetism can be fitted quite well using values of the energy band parameters which give agreement with the de Haas-van Alphen effect, optical absorption, and magnetoreflection experiments.
92 citations
"The electronic properties of graphe..." refers background in this paper
...of trigonal warping and showed that the low temperature diamagnetism increases (Sharma et al., 1974)....
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...Later Sharma et al. extended the al- ulation of M Clure for graphite by in luding the e e t of trigonal warping and showed that the low temperaturediamagnetism in reases (Sharma et al., 1974)....
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TL;DR: In this article, the critical wave function of a two-dimensional Dirac fermion in the presence of a random magnetic field is calculated in terms of thermodynamic functions, such as free energy and entropy, which coincide exactly with those of a generalized random energy model.
Abstract: The multifractal scaling exponents are calculated for the critical wave function of a two-dimensional Dirac fermion in the presence of a random magnetic field. It is shown that the problem of calculating the multifractal spectrum maps into the thermodynamics of a static particle in a random potential. The multifractal exponents are simply given in terms of thermodynamic functions, such as free energy and entropy, which are argued to be self-averaging in the thermodynamic limit. These thermodynamic functions are shown to coincide exactly with those of a generalized random energy model, in agreement with previous results obtained using Gaussian field theories in an ultrametric space.
92 citations
"The electronic properties of graphe..." refers background in this paper
...The one ele tron nature of this two dimensionalproblem makes it possible, at the Dira energy, to mapit onto models of intera ting ele trons in one dimension,where many exa t results an be obtained (Castillo et al.,1997)....
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TL;DR: In this paper, the exact Landau level structure of graphite has been obtained for the magnetic field parallel to the c -axis with the aid of numerical calculation, and a new de Haas-van Alphen oscillation of the minority hole is predicted and connected with another magnetic breakthrough effect due also to trigonal warping.
Abstract: The exact Landau level structure of graphite has been obtained for the magnetic field parallel to the c -axis with the aid of the numerical calculation. Special emphasis is layed on the effect of the trigonal warping in band structure which has been treated approximately up to the present. The peculiar behaviour of Landau levels in low fields can be understood in terms of the magnetic breakthrough phenomenon. A new de Haas-van Alphen oscillation of the minority hole is predicted and connected with another magnetic breakthrough effect due also to the trigonal warping.
91 citations
"The electronic properties of graphe..." refers background in this paper
...The ele troni spe trum of the model an also be al ulated in a magneti eld (de Gennes,1964; Nakao, 1976), and the results are also onsistentwith STM on graphite surfa es (Kobayashi et al., 2005;Li and Andrei, 2007; Matsui et al., 2005; Niimi et al.,2006), epitaxially grown graphene sta ks (Mallet et…...
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...The ele troni spe trum of the model an also be al ulated in a magneti eld (de Gennes,1964; Nakao, 1976), and the results are also onsistentwith STM on graphite surfa es (Kobayashi et al., 2005;Li and Andrei, 2007; Matsui et al., 2005; Niimi et al.,2006), epitaxially grown graphene sta ks (Mallet et al.,2007), and with opti al measurements in the infraredrange (Li et al., 2006)....
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TL;DR: The trigonal warping of the dispersion relation around the valleys in the Brillouin zone is effective only for low-energy excitations, and its role cannot be neglected in the zero-energy minimal conductivity of bilayer graphene.
Abstract: Using a reformulated Kubo formula we calculate the zero-energy minimal conductivity of bilayer graphene taking into account the small but finite trigonal warping. We find that the conductivity is independent of the strength of the trigonal warping and it is 3 times as large as that without trigonal warping and 6 times larger than that in single layer graphene. Although the trigonal warping of the dispersion relation around the valleys in the Brillouin zone is effective only for low-energy excitations, our result shows that its role cannot be neglected in the zero-energy minimal conductivity.
89 citations
"The electronic properties of graphe..." refers background in this paper
...Similar e e ts an o ur in graphene quantum dots, where the in-ner and outer regions ontain ele trons and holes, re-spe tively (Cserti et al., 2007b)....
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...Moreover, this orresponden e remains valid for the ase of a bilayer without and with trigonal warping e e ts(Cserti et al., 2007a; Koshino and Ando, 2006)....
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Posted Content•
TL;DR: In this article, the authors suggest that the physics underlying the removal of sublattice and spin degeneracies in graphene in a strong magnetic field describes a phase transition connected with the generation of excitonic and spin gaps.
Abstract: We suggest that physics underlying the recently observed removal of sublattice and spin degeneracies in graphene in a strong magnetic field describes a phase transition connected with the generation of excitonic and spin gaps. The strong-coupling regime is described using a phenomenological model with enhanced Zeeman splitting (spin gap) and excitonic gaps. The experimental form of the Hall conductivity $\sigma_{xy}$ with the additional $
u= 0, \pm 1$ plateaus is reproduced. The form of $\sigma_{xy}$ in the case of a strong-coupling regime with no enhanced Zeeman splitting is also discussed.
88 citations
"The electronic properties of graphe..." refers background in this paper
...In addition to phases with enhan ed ferromag-netism or with broken valley symmetry, intera tionsat high magneti elds an lead to ex itoni instabil-ities (Gusynin et al., 2006) and Wigner rystal phases(Zhang and Joglekar, 2007)....
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