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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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Citations
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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 ArticleDOI
TL;DR: It is shown that electron transport in the integer quantum Hall effect (QHE) in graphene is dominated by counterpropagating edge states and the existence of gapless edge states puts stringent constraints on possible theoretical models of the nu=0 state.
Abstract: We report on the unusual nature of the nu=0 state in the integer quantum Hall effect (QHE) in graphene and show that electron transport in this regime is dominated by counterpropagating edge states. Such states, intrinsic to massless Dirac quasiparticles, manifest themselves in a large longitudinal resistivity rho(xx) > or approximately h/e(2), in striking contrast to rho(xx) behavior in the standard QHE. The nu=0 state in graphene is also predicted to exhibit pronounced fluctuations in rho(xy) and rho(xx) and a smeared zero Hall plateau in sigma(xy), in agreement with experiment. The existence of gapless edge states puts stringent constraints on possible theoretical models of the nu=0 state.

218 citations


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

  • ...The result-ing level rossing between an ele tron like level with spinanti-parallel to the eld, and a hole like level with spinparallel to the eld, may lead to Luttinger liquid featuresin the edge states (Abanin et al., 2007b; Fertig and Brey,2006)....

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  • ...In the presen e of a magneti eld, when the bulk states are gapped, the edge statesare responsible for the transport of spin and harge(Abanin et al., 2006, 2007a; Abanin and Levitov, 2007;Abanin et al., 2007b)....

    [...]

  • ...The ombination of disorder and a magneti eld may also lift the degenera y be-tween the two valleys, favoring valley polarized phases(Abanin et al., 2007a)....

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  • ...…val-ley or spin degenera y of the Landau levels, whi h anbe observed in spe tros opy measurements (Jiang et al.,2007a; Sadowski et al., 2006), or in the appearan eof new quantum Hall plateaus (Abanin et al., 2007b;Giesbers et al., 2007; Goswami et al., 2007; Jiang et al.,2007b; Zhang et al., 2006)....

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Journal ArticleDOI
TL;DR: In this article, the room temperature Raman signatures from graphene layers on sapphire and glass substrates were compared with those from graphene on GaAs substrate and on the standard Si/SiO2 substrate, which served as a reference.
Abstract: The room-temperature Raman signatures from graphene layers on sapphire and glass substrates were compared with those from graphene on GaAs substrate and on the standard Si/SiO2 substrate, which served as a reference. It was found that while G peak of graphene on Si/SiO2 and GaAs is positioned at 1580 cm -1 it is down-shifted by ~5 cm -1 for graphene-on-sapphire (GOS) and, in many cases, splits into doublets for graphene-on-glass (GOG) with the central frequency around 1580 cm -1 . The obtained results are important for graphene characterization and its proposed graphene applications in electronic devices.

217 citations


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

  • ...…et al.,2007; Peres et al., 2007a) (in analogy with what hasbeen done in nanotubes (Stephan et al., 1994)); usingdi erent substrates that modify the ele troni stru -ture (Calizo et al., 2007; Das et al., 2007; Faugeras et al.,2007; Giovannetti et al., 2007; Var hon et al., 2007;Zhou et al., 2007)....

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Journal ArticleDOI
TL;DR: In this paper, the effects of the electron-electron interactions in a graphene layer are investigated and it is shown that short-range couplings are irrelevant and scale towards zero at low energies, due to the vanishing of density of states at the Fermi level.
Abstract: The effects of the electron-electron interactions in a graphene layer are investigated. It is shown that short-range couplings are irrelevant and scale towards zero at low energies, due to the vanishing of density of states at the Fermi level. Topological disorder enhances the density of states and can lead to instabilities. In the presence of sufficiently strong repulsive interactions, p-wave superconductivity can emerge.

215 citations


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

  • ...This model is easily generalizable to a sta k of semimet-als des ribed by the 2D Dira equation (González et al.,2001)....

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  • ...This model is easily generalizable to a stack of semimetals described by the 2D Dirac equation (González et al., 2001)....

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  • ...to mixing of the K and K ′ wavefunctions, leading to a gauge field like the one induced by a pentagon (González et al., 2001)....

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  • ...In general, a lo al rotation of the axes of the hon-ey omb latti e indu es hanges in the hopping whi hlead to mixing of the K and K ′ wavefun tions, lead-ing to a gauge eld like the one indu ed by a pen-tagon (González et al., 2001)....

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Journal ArticleDOI
TL;DR: It is found that flexural phonons dominate the phonon contribution to the resistivity rho below a crossover temperature T(x) where they obtain an anomalous temperature dependence rho proportional, variantT(5/2)lnT.
Abstract: Rotation and reflection symmetries impose that out-of-plane (flexural) phonons of freestanding graphene membranes have a quadratic dispersion at long wavelength and can be excited by charge carriers in pairs only. As a result, we find that flexural phonons dominate the phonon contribution to the resistivity $\ensuremath{\rho}$ below a crossover temperature ${T}_{x}$ where we obtain an anomalous temperature dependence $\ensuremath{\rho}\ensuremath{\propto}{T}^{5/2}\mathrm{ln} T$. The logarithmic factor arises from renormalizations of the flexural-phonon dispersion due to coupling between bending and stretching degrees of freedom of the membrane.

213 citations

Journal ArticleDOI
TL;DR: In this article, the first non-local four-probe experiments on graphene contacted by ferromagnetic Permalloy electrodes were performed, and the nonlocal resistance signal can be observed up to at least T = 300 K.
Abstract: Graphitic nanostructures, e.g. carbon nanotubes (CNT) and graphene, have been proposed as ideal materials for spin conduction[1-7]; they have long electronic mean free paths[8] and small spin-orbit coupling[9], hence are expected to have very long spin-scattering times. In addition, spin injection and detection in graphene opens new opportunities to study exotic electronic states such as the quantum Hall[10,11] and quantum spin Hall[9] states, and spin-polarized edge states[12] in graphene ribbons. Here we perform the first non-local four-probe experiments[13] on graphene contacted by ferromagnetic Permalloy electrodes. We observe sharp switching and often sign-reversal of the non-local resistance at the coercive field of the electrodes, indicating definitively the presence of a spin current between injector and detector. The non-local resistance changes magnitude and sign quasi-periodically with back-gate voltage, and Fabry-Perot-like oscillations[6,14,15] are observed, consistent with quantum-coherent transport. The non-local resistance signal can be observed up to at least T = 300 K.

213 citations


Additional excerpts

  • ...The amazingtransport properties of graphene allow for their use ina plethora of appli ations ranging from single mole uledete tion (S hedin et al., 2007; Wehling et al., 2007)to spin inje tion (Cho et al., 2007; Hill et al., 2007;Ohishi et al., 2007; Tombros et al., 2007)....

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