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 optical visibility of monolayer and bilayer graphene was modeled on a SiO2∕Si substrate or thermally annealed on the surface of SiC.
Abstract: The authors model the optical visibility of monolayer and bilayer graphene deposited on a SiO2∕Si substrate or thermally annealed on the surface of SiC. Visibility is much stonger in reflection than in transmission, reaching the optimum conditions when the bare substrate transmits light resonantly. In the optical range of frequencies a bilayer is approximately twice as visible as a monolayer thereby making the two types of graphene distinguishable from each other.
294 citations
"The electronic properties of graphe..." refers background in this paper
...Graphene was even-tually spotted due to the subtle opti al e e t it reates ontop of a leverly hosen SiO2 substrate (Novoselov et al.,2004) that allows its observation with an ordinary opti- al mi ros ope (Abergel et al., 2007; Blake et al., 2007;Casiraghi et al., 2007)....
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TL;DR: The critical behavior of disordered degenerate semiconductors is studied within a mean-field theory valid when the number of degeneracy points is large and it is shown that above two dimensions there is a semimetal-metal transition at a critical impurity concentration.
Abstract: The critical behavior of disordered degenerate semiconductors is studied within a mean-field theory valid when the number of degeneracy points is large I show that above two dimensions there is a semimetal-metal transition at a critical impurity concentration The mean free path and the one-particle density of states exhibit scaling behavior with universal exponents The transition is smeared at nonzero temperature An equation of state, relating temperature, disorder, and bare conductivity, is presented In two dimensions, the semimetallic phase is unstable I show that a localization transition follows except in two dimensions where all states are localized The bare conductivity appears to be a universal number in two dimensions Applications to zero-gap semiconductors and other systems are discussed
293 citations
"The electronic properties of graphe..." refers background in this paper
...When the Fermi energy is at the Dira point, a repli aanalysis shows that the ondu tivity approa hes a uni-versal value of the order of e2/h (Fradkin, 1986a,b)....
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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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TL;DR: In this article, the effect of the ripples and an external magnetic field on the low energy electronic structure of graphene was studied and it was shown that zero-energy Landau levels will form, associated with the smooth deformation of the graphene layer, when the height corrugation, $h$, and the length of the ripple, $l$, are such that ${h}^{2}∕la\ensuremath{\gtrsim}1$, where $a$ is the lattice constant.
Abstract: We study the changes induced by the effective gauge field due to ripples on the low energy electronic structure of graphene. We show that zero-energy Landau levels will form, associated with the smooth deformation of the graphene layer, when the height corrugation, $h$, and the length of the ripple, $l$, are such that ${h}^{2}∕la\ensuremath{\gtrsim}1$, where $a$ is the lattice constant. The existence of localized levels gives rise to a large compressibility at zero energy and to the enhancement of instabilities arising from electron-electron interactions including electronic phase separation. The combined effect of the ripples and an external magnetic field breaks the valley symmetry of graphene, leading to the possibility of valley selection.
290 citations
TL;DR: In this article, a scanning-tunneling microscopy (STM) study of a gently graphitized $6H\text{\ensuremath{-}}\mathrm{Si}\mathrm {C}(0001)$ surface in ultrahigh vacuum is presented.
Abstract: We present a scanning-tunneling microscopy (STM) study of a gently graphitized $6H\text{\ensuremath{-}}\mathrm{Si}\mathrm{C}(0001)$ surface in ultrahigh vacuum. From an analysis of atomic scale images, we identify two different kinds of terraces, which we attribute to mono- and bilayer graphene capping a C-rich interface. At low temperature, both terraces show $(\sqrt{3}\ifmmode\times\else\texttimes\fi{}\sqrt{3})$ quantum interferences generated by static impurities. Such interferences are a fingerprint of $\ensuremath{\pi}$-like states close to the Fermi level. We conclude that the metallic states of the first graphene layer are almost unperturbed by the underlying interface, in agreement with recent photoemission experiments [Bostwick et al., Nat. Phys. 3, 36 (2007)].
287 citations
"The electronic properties of graphe..." refers background in this paper
...Lo al probesreveal a ri h stru ture of terra es (Mallet et al., 2007)and interferen e patterns due to defe ts at or below thegraphene layers (Rutter et al., 2007)....
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..., 2006), epitaxially grown graphene stacks (Mallet et al., 2007), and with optical measurements in the infrared range (Li et al....
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...Local probes reveal a rich structure of terraces (Mallet et al., 2007) and interference patterns due to defects at or below the graphene layers....
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...…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: Using quantum Monte Carlo and finite-size scaling for the Hubbard model, this paper found evidence of a zero-temperature transition between the nonmagnetic semi-metal and an antiferromagnetic insulator in the 2D honeycomb lattice for a nontrivial value of U/t?=?4.5???0.5.
Abstract: Using quantum Monte Carlo and finite-size scaling for the Hubbard model, we find evidence of a zero-temperature transition between the nonmagnetic semi-metal and an antiferromagnetic insulator in the 2D honeycomb lattice for a nontrivial value of U/t?=?4.5???0.5. The corresponding transition in Hartree-Fock mean field is at U/t?=?2.23, which indicates the importance of quantum fluctuations. This represents the first example of Mott-Hubbard transition in a 2D bipartite lattice. Similar transitions are predicted for special lattices in higher dimensions, in particular for the 3D diamond lattice.
281 citations
"The electronic properties of graphe..." refers background in this paper
...(225)Quantum Monte Carlo al ulations (Paiva et al., 2005;Sorella and Tosatti, 1992), raise however its value to: UAF (0) ≃ 5t ....
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...Quantum Monte Carlo calculations (Paiva et al., 2005; Sorella and Tosatti, 1992), raise however its value to:...
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...This result gives a finite UAF at the neutrality point (Martelo et al., 1997; Sorella and Tosatti, 1992):...
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...This result gives a -nite UAF at the neutrality point (Martelo et al., 1997;Sorella and Tosatti, 1992): UAF (0) = 2.23t ....
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