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Journal ArticleDOI

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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Journal ArticleDOI
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

Journal ArticleDOI
19 Jun 2009-Science
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

Journal ArticleDOI
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

Journal ArticleDOI
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

Journal ArticleDOI
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

References
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Journal Article
TL;DR: Ohta et al. as mentioned in this paper derived the stacking order, layer-dependent electron potential, screening length and strength of interlayer interaction by comparison with tight binding calculations, yielding a comprehensive description of multilayer graphene's electronic structure.
Abstract: Interlayer interaction and electronic screening in multilayer graphene Taisuke Ohta, 1, 2 Aaron Bostwick, 1 J. L. McChesney, 1, 3 Thomas Seyller, 4 Karsten Horn, 2 and Eli Rotenberg 1 Advanced Light Source, Lawrence Berkeley National Laboratory, Berkeley, California, USA Fritz-Haber-Institut der Max-Planck-Gesellschaft, Berlin, Germany Montana State University, Bozeman, Montana, USA Institut f¨ r Physik der Kondensierten Materie, Universit¨ t Erlangen-N¨ rnberg, Erlangen, Germany u a u (Dated: March 30, 2007) The unusual transport properties of graphene are the direct consequence of a peculiar bandstruc- ture near the Dirac point. We determine the shape of the π bands and their characteristic splitting, and find the transition from two-dimensional to bulk character for 1 to 4 layers of graphene by angle-resolved photoemission. By detailed measurements of the π bands we derive the stacking order, layer-dependent electron potential, screening length and strength of interlayer interaction by comparison with tight binding calculations, yielding a comprehensive description of multilayer graphene’s electronic structure. PACS numbers: Much recent attention has been given to the electronic structure of multilayer films of graphene, the honeycomb carbon sheet which is the building block of graphite, car- bon nanotubes, C 60 , and other mesoscopic forms of car- bon [1]. Recent progress in synthesizing or isolating mul- tilayer graphene films [2–4] has provided access to their physical properties, and revealed many interesting trans- port phenomena, including an anomalous quantum Hall effect [5, 6], ballistic electron transport at room temper- ature [7], micron-scale coherence length [7, 8] and novel many-body couplings [9]. These effects originate from the effectively massless Dirac Fermion character of the carri- ers derived from graphene’s valence bands, which exhibit a linear dispersion degenerate near the so-called Dirac point energy, E D [10]. These unconventional properties of graphene offer a new route to room temperature, molecular-scale electron- ics capable of quantum computing [6, 7]. For example, a possible switching function in bilayer graphene has been suggested by reversibly lifting the band degeneracy at the Fermi level (E F ) upon application of an electric field [11, 12]. This effect is due to a unique sensitivity of the bandstructure to the charge distribution brought about by the interplay between strong interlayer hopping and weak interlayer screening, neither of which are currently well-understood [13, 14]. In order to evaluate the interlayer screening, stack- ing order and interlayer coupling, we have systemati- cally studied the evolution of the bandstructure of one to four layers of graphene using angle-resolved photoemis- sion spectroscopy (ARPES). We demonstrate experimen- tally that the interaction between layers and the stacking sequence affect the topology of the π bands, the former inducing an electronic transition from two-dimensional (2D) to 3D (bulk) character when going from one layer to multilayer graphene. The interlayer hopping integral and screening length are determined as a function of the num- ber of graphene layers by exploiting the sensitivity of π FIG. 1: (color online) Photoemission images revealing the bandstructure of (a) single and (b) bilayer graphene along high symmetry directions, Γ-K-M-Γ. The blue dashed lines are scaled DFT bandstructure of free standing films [16]. Inset in (a) shows the 2D Brillouin zone of graphene. states to the Coulomb potential, and the layer-dependent carrier concentration is estimated. The films were synthesized on n-type (nitrogen, 1 × 10 18 cm −3 ) 6H-SiC(0001) substrates (SiCrystal AG) that were etched in hydrogen at 1550 C. Annealing in a vac- uum first removes the resulting silicate adlayer and then causes the growth of the graphene layers between 1250 to 1400 C [15]. Beyond the first layer, the samples have a ± 0.5 monolayer thickness variation; the bandstructures of different thicknesses were extracted using the method of Ref. [11]. ARPES measurements were conducted at the Electronic Structure Factory endstation at beamline 7.01 of the Advanced Light Source, equipped with a Sci- enta R4000 electron energy analyzer. The samples were cooled to ∼ 30K by liquid He. The photon energy was 94 eV with the overall energy resolution of ∼30 meV for Fig. 1 and Fig. 2(a-d). The bandstructures of a single (Fig. 1 (a)) and a bi-

533 citations

Journal ArticleDOI
TL;DR: In this article, the interplay between crystalline (or hexatic) order and thermal fluctuations in membranes with vanishing surface tension is studied, and a finite temperature crumpling transition is predicted for crystalline membranes.
Abstract: We study the interplay between crystalline (or hexatic) order and thermal fluctuations in membranes with vanishing surface tension. If the connectivity of the crystalline state is preserved, the membrane remains uncrumpled at low temperatures. When dislocations are allowed, however, screening of elastic stresses by buckling reduces dislocation energies, and promotes dislocation unbinding. When the resulting hexatic phase is stable, the stiffness associated with orientational correlations leads to a logarithmic enhancement of the bending rigidity which counteracts the thermal softening found in fluid surfaces. A finite temperature crumpling transition is predicted for crystalline membranes, and possibly for hexatic membranes as well.

529 citations


"The electronic properties of graphe..." refers background in this paper

  • ...…and in-plane modes(or 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…...

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Journal ArticleDOI
TL;DR: It is shown that vacancies induce the formation of localized states in the half-filled honeycomb lattice when particle-hole symmetry is broken, and localized states become resonances close to the Fermi level.
Abstract: We consider the electronic structure near vacancies in the half-filled honeycomb lattice. It is shown that vacancies induce the formation of localized states. When particle-hole symmetry is broken, localized states become resonances close to the Fermi level. We also study the problem of a finite density of vacancies, obtaining the electronic density of states, and discussing the issue o f electronic localization in these systems. Our results have also relevance for the problem of disorder in d-wave superconductors. Introduction. The problem of disorder in systems with Dirac fermions has been studied extensively in the last few years in the context of dirty d-wave superconductors (1). Dirac fermions are also the elementary excitations of the hon- eycomb lattice at half-filling, equally known as graphene, which is realized in two-dimensional (2D) Carbon based ma- terials with sp 2 bonding. It is well-known that disorder is ubiquitous in graphene and graphite (which is produced by stacking graphene sheets) and its effect on the electronic s truc- ture has been studied extensively (2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13). It has been shown recently (14) that the interplay of disorder and electron-electron interactions is fundame ntal for the understanding of recent experiments in graphene de- vices (15). Furthermore, experiments reveal that ferromag- netism is generated in heavily disordered graphite samples (16, 17, 18, 19, 20), but the understanding of the interplay of strong disorder and electron-electron interactions in t hese systems is still in its infancy. Different mechanisms for fe rro- magnetism in graphite have been proposed and they are either based on the nucleation of ferromagnetism around extended defects such as edges (2, 8, 12, 13) or due to exchange in- teractions originating from unscreened Coulomb interactions (21). Therefore, the understanding of the nature of the elec- tronic states in Dirac fermion systems with strong disorder is of the utmost interest. In the following, we analyze in detail states near the Fermi energy induced by vacancies in a tight-binding model for the electronic states of graphene planes. We show that single va- cancies in a graphene plane generate localized states which are sensitive to the presence of particle-hole symmetry break- ing. Moreover, a finite density of such defects leads to stron g changes in the local and averaged electronic Density Of States (DOS) with the creation of localized states at the Dirac point. The model. We consider a single band model described by the Hamiltonian:

514 citations


"The electronic properties of graphe..." refers background in this paper

  • ...Furthermore, wewill only fo us on the problem of short range s atter-ing in the unitary limit sin e in this regime many an-alyti al results are obtained (Kumazaki and Hirashima, 2006; Mariani et al., 2007; Pereira et al., 2006, 2007a;Peres et al., 2006 ; Skrypnyk and Loktev, 2006, 2007)....

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  • ...A dis rete version ofthese states an be realized in a nearest neighbor tight-binding model with unitary s atterers su h as va an ies(Pereira et al., 2006)....

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Journal ArticleDOI
TL;DR: In this paper, a self-consistent Born approximation of the density of states and the conductivity of undoped systems in magnetic fields is proposed, where the quantum theory provides results quite different from the results of Boltzmann transport theory even in the absence of a magnetic field.
Abstract: In a self-consistent Born approximation, the density of states and the conductivity are calculated in a two-dimensional graphite sheet in magnetic fields. Two different cases of scatterers are considered, the short-range case where the range is smaller than the lattice constant and the long-range case where it is comparable or slightly larger. The quantum theory provides results quite different from the results of Boltzmann transport theory even in the absence of a magnetic field. In high magnetic fields, the conductivity exhibits a series of peaks, whose values depend only on the natural constants and the Landau level index. The conductivity of undoped systems is always given by a universal conductivity \(e^{2}/\pi^{2}\hbar\) independent of a magnetic field.

508 citations


"The electronic properties of graphe..." refers background or methods or result in this paper

  • ...Koshino and Ando onsidered the diamagnetismof disordered graphene in the self onsistent Born approx-imation, with a disorder potential of the form U(r) = 1uiδ(r − R) (Koshino and Ando, 2007)....

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  • ...(170)The lo al displa ements of the atoms in the unit ell anbe related to u(r) by (Ando, 2006a): (~δab · ∇)u = κ−1(uA − uB) , (171)where κ is a dimensionless quantity that depends on mi- ros opi details....

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  • ...Ele tron-phonon oupling has also been investigated the-oreti ally in the ase of a nite magneti eld (Ando,2007a; Goerbig et al., 2007)....

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  • ...Koshino, M., and T. Ando, 2006, Phys....

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  • ...Ando, T., 2006b, J. Phys....

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Journal ArticleDOI
TL;DR: In this paper, the electronic properties and relative stabilities of edge-oxidized zigzag graphene nanoribbons were studied and the oxidation schemes considered include hydroxyl, l...
Abstract: We present a comprehensive theoretical study of the electronic properties and relative stabilities of edge-oxidized zigzag graphene nanoribbons. The oxidation schemes considered include hydroxyl, l...

500 citations