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, an effective mass Hamiltonian for carbon nanotubes in the presence of a weak spin-orbit interaction has been derived, which gives rise to terms corresponding to a kind of a spin-Zeeman energy due to magnetic fields in the circumference and axis direction.
Abstract: An effective-mass Hamiltonian is derived for carbon nanotubes in the presence of a weak spin-orbit interaction. The spin-orbit interaction gives rise to terms corresponding to a kind of a spin-Zeeman energy due to magnetic fields in the circumference and axis direction. As a result spin scattering is induced even by spin-independent scatterers.
240 citations
"The electronic properties of graphe..." refers background in this paper
...When the inver-sion symmetry of the honey omb latti e is broken, ei-ther be ause the graphene layer is urved or be ausean external ele tri eld is applied (Rashba intera tion)additional terms, whi h modulate the nearest neigh-bor hopping, are indu ed (Ando, 2000)....
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TL;DR: In this paper, the authors investigated the influence of substrates on Raman scattering spectrum from graphene and found that while G peak of graphene on Si∕SiO2 and GaAs is positioned at 1580cm−1, it is downshifted by ∼5 cm−1 for graphene on sapphire and, in some cases, splits into doublets for G peak on glass with the central frequency around 1580mm−1.
Abstract: The authors investigated the influence of substrates on Raman scattering spectrum from graphene. The room-temperature Raman signatures from graphene layers on GaAs, sapphire, and glass substrates were compared with those from graphene on the standard Si∕SiO2 (300nm) substrate, which served as a reference. It was found that while G peak of graphene on Si∕SiO2 and GaAs is positioned at 1580cm−1, it is downshifted by ∼5cm−1 for graphene on sapphire and, in some cases, splits into doublets for graphene on glass with the central frequency around 1580cm−1. The obtained results are important for nanometrology of graphene and graphene-based devices.
239 citations
TL;DR: The quantum de Haas-van Alphen (dHvA) and Shubnikov-de Haas oscillations measured in graphite were decomposed by pass-band filtering onto contributions from three different groups of carriers, identified as minority holes having a 2D parabolic massive spectrum and massive majority electrons with a 3D spectrum.
Abstract: The quantum de Haas--van Alphen (dHvA) and Shubnikov--de Haas oscillations measured in graphite were decomposed by pass-band filtering onto contributions from three different groups of carriers. Generalizing the theory of dHvA oscillations for 2D carriers with an arbitrary spectrum and by detecting the oscillation frequencies using a method of two-dimensional phase-frequency analysis which we developed, we identified these carriers as (i) minority holes having a 2D parabolic massive spectrum ${p}_{\ensuremath{\perp}}^{2}/2{m}_{\ensuremath{\perp}}$, (ii) massive majority electrons with a 3D spectrum and (iii) majority holes with a 2D Dirac-like spectrum $\ifmmode\pm\else\textpm\fi{}v{p}_{\ensuremath{\perp}}$ which seems to be responsible for the unusual strongly-correlated electronic phenomena in graphite.
239 citations
TL;DR: In this article, the conduction-electron diamagnetism was calculated for the three-dimensional band structure of graphite and the susceptibility calculated by analytically carrying out the free energy sum.
Abstract: The conduction-electron diamagnetism was calculated for the three- dimensional band structure of graphite. The magnetic energy levels are found and the susceptibility calculated by analytically carrying out the free energy sum. Agreement with experiment is found for values of the band parameters nearly equal to those which give agreement with the de Haas-van Alphen effect and other phenomena. The value of gamma /sub 0/ is found to be 2.8 plus or minus 0.1 ev. The results indicate the gamma /sub 1/ is about 0.27 ev and DELTA is about 0.025. The other band parameters do not have an important influence upon the value of the susceptibility. The relation to the general treatments of conduction-electron diamagnetism is also discussed. (auth)
238 citations
"The electronic properties of graphe..." refers methods in this paper
...McClure (McClure, 1956) computed diamagnetism of a 2D honeycomb lattice using the theory introduced by Wallace (Wallace, 1947), a calculation he later generalized to three dimensional graphite (McClure, 1960)....
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TL;DR: A theory is developed that explains a strong asymmetry in the tunneling current between neighboring carbon atoms in the hexagonal ring as a purely electronic effect, arising from the symmetry of the states scanned by the STM, which dominates over the topography of graphite.
Abstract: Images of the (0001) surface of graphite observed in the scanning-tunneling microscope (STM) show a strong asymmetry in the tunneling current between neighboring carbon atoms in the hexagonal ring. The magnitude of this asymmetry is seen to be almost independent of the polarity and to decrease slightly with increasing amplitude of the bais voltage for voltages below 1 V. A theory is developed that explains this anomaly as a purely electronic effect, arising from the symmetry of the states scanned by the STM, which dominates over the topography of graphite. The predicted trends for the bias-voltage dependence of the asymmetry are confirmed experimentally.
238 citations
"The electronic properties of graphe..." refers result in this paper
...Furthermore, it is well known that in graphite theplanes an be rotated relative ea h other giving rise toMoiré patterns that are observed in STM of graphite sur-fa es (Rong and Kuiper, 1993)....
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...This pi ture has been on rmed by STM measurementson graphene (Ishigami et al., 2007; Stolyarova et al.,2007) in whi h strong orrelations were found betweenthe roughness of the substrate and the graphene topog-raphy....
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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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...This result is onsistent with the well known fa tthat only one of the two sublatti es at a graphite surfa e an be resolved by s anning tunneling mi ros opy (STM)(Tománek et al., 1987)....
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...This result is consistent with the well known fact that only one of the two sublattices at a graphite surface can be resolved by scanning tunneling microscopy (STM) (Tománek et al., 1987)....
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