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, the surface density of positively and negatively charged impurities that limit the mobility in a graphene monolayer is determined based on the exact result for the transport cross section.
Abstract: A method is suggested to separately determine the surface density of positively and negatively charged impurities that limit the mobility in a graphene monolayer. The method is based on the exact result for the transport cross section, according to which the massless carriers are scattered more strongly when they are attracted to a charged impurity than when they are repelled from it.
128 citations
"The electronic properties of graphe..." refers background or methods or result in this paper
...Thesolution of the Dira equation for the Coulomb poten-tial in 2D an be studied analyti ally (Biswas et al.,2007; DiVin enzo and Mele, 1984; Novikov, 2007a;Pereira et al., 2007b; Shytov et al., 2007)....
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...…based on s reened harged impurities it ispossible to obtain from a Boltzmann equation ap-proa h a ondu tivity varying linearly with the den-sity, in agreement with the experimental result (Ando,2006b; Katsnelson and Geim, 2008; Novikov, 2007b;Peres et al., 2007b; Trushin and S hliemann, 2007)....
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...Passivation an be modeled in thetight-binding approa h by modi ations of the hoppingenergies (Novikov, 2007 ) or via additional phases in theboundary onditions (Kane and Mele, 1997)....
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TL;DR: In this article, a least square fitting to a generalized Landau formula was used to determine the electron Fermi surfaces in a graphite single crystal, and the results were analyzed by a least-squares fitting.
Abstract: Measurements of the oscillatory magnetoresistance of a high-quality graphite single crystal were made for all angles $\ensuremath{\theta}$ between the magnetic field and the $c$ axis, for magnetic fields up to 24 kG, and for temperatures from 1.22 to 4.22\ifmmode^\circ\else\textdegree\fi{}K. The results were analyzed by a least-squares fitting to a generalized Landau formula. Oscillations due to electrons were observed for all orientations (including H \ensuremath{\perp} c, where the amplitude dropped by a factor ${10}^{5}$), proving that the electron Fermi surfaces are closed. Although oscillations due to holes were not observed beyond $\ensuremath{\theta}\ensuremath{\simeq}84\ifmmode^\circ\else\textdegree\fi{}$, indirect arguments show that the hole Fermi surfaces are also closed. Both electron and hole surfaces are elongated along the $c$ axis and have anisotropy ratios of 12.1\ifmmode\pm\else\textpm\fi{}1.4 and about 17, respectively. The electron surface is approximately ellipsoidal, whereas the hole surface is similar except for extended ends giving it a diamond-like shape. The results are consistent with a moderate degree of trigonal asymmetry about the $c$ axis. Comparison between the electron density found from the volume of the electron Fermi surfaces and that determined previously from the nonoscillatory galvanomagnetic data confirms the theoretical prediction that there are four electron Fermi surfaces in the Brillouin zone. More indirect arguments show that there are two hole surfaces. Consideration of the size and location of these surfaces along the six zone edges parallel to the $c$ axis leads to a new determination of $\ensuremath{\Delta}\ensuremath{\simeq}\ensuremath{-}0.12$ eV for the band parameter which represents the difference of potential between the two types of atomic sites in the graphite lattice. Analysis of the temperature and magnetic field dependence of the oscillatory amplitude yields effective mass values in the basal plane of $(0.039\ifmmode\pm\else\textpm\fi{}0.001){m}_{0}$ for electrons and $(0.057\ifmmode\pm\else\textpm\fi{}0.002){m}_{0}$ for holes. These masses show an orientation dependence that is consistent with the derived Fermi surface anisotropies. The large amplitude and asymmetric shape of the oscillations in the magnetoconductivity, measured for H\ensuremath{\parallel}c at 1.26 and 4.22\ifmmode^\circ\else\textdegree\fi{}K, are accurately described by the theory of Adams and Holstein. However, there is an unexplained monotonic variation with magnetic field in the total magnetoconductivity. The effective change in temperature due to collision broadening $\ensuremath{\Delta}T$ is about 5 times greater than that estimated from the conductivity relaxation time. This discrepancy in $\ensuremath{\Delta}T$ is qualitatively explained and is related directly to the fact, established from the data of Berlincourt and Steele, that the $\ensuremath{\Delta}T$ found from magnetoresistance oscillations is greater than that found from susceptibility oscillations on the same sample.
128 citations
"The electronic properties of graphe..." refers background or methods in this paper
...Re ent ARPESexperiments (Bostwi k et al., 2007b; Ohta et al., 2006;Zhou et al., 2006a, ) performed in epitaxially growngraphene sta ks (Berger et al., 2004) on rm the mainfeatures of this model, formulated mainly on the ba-sis of Fermi surfa e measurements (M Clure, 1957;Soule et al., 1964)....
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...Weiss-McClure (SWM) band structure of graphite which provided a detailed description of the electronic properties in this material (McClure, 1957; Slonczewski and Weiss, 1958) and was very successful in describing the experimental data (Boyle and Nozières, 1958; Dillon et al., 1977; McClure, 1958; Soule et al., 1964; Spry and Scherer, 1960; Williamson et al., 1965)....
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...The values of these parameters, and their dependence with pressure, or, equivalently, the interatomic distances, have been extensively studied (Dillon et al., 1977; Dresselhaus and Mavroides, 1964; McClure, 1957; Nozières, 1958; Soule et al., 1964)....
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...…ription of the ele troni properties in this mate-rial (M Clure, 1957; Slon zewski and Weiss, 1958) andwas very su essful in des ribing the experimental data(Boyle and Nozières, 1958; Dillon et al., 1977; M Clure,1958, 1964; Soule et al., 1964; Spry and S herer, 1960;Williamson et al., 1965)....
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...The values ofthese parameters, and their dependen e with pressure,or, equivalently, the interatomi distan es, have been ex-tensively studied (Brandt et al., 1988; Dillon et al., 1977;Dresselhaus and Mavroides, 1964; M Clure, 1957, 1964;Nozières, 1958; Soule et al., 1964)....
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TL;DR: In this article, a string equation describing the possible existing shapes of the axis curve of multishell carbon tubes (MCTs) is obtained in the continuum limit by minimizing the shape energy.
Abstract: To study the shape formation process of carbon nanotubes, a string equation describing the possible existing shapes of the axis curve of multishell carbon tubes (MCTs) is obtained in the continuum limit by minimizing the shape energy. It is shown that there exists a threshold relation of the outmost and inmost radii that gives a parameter regime in which a straight MCT will be bent or twisted. Among the deformed shapes, the regular coiled MCTs are shown to be one of the solutions of the string equation. In particular, the optimal ratio of pitch p and radius r(0) for such a coil is found to be equal to 2 pi, which is in good agreement with recent observation of coil formation in MCTs by Zhang et al.
127 citations
"The electronic properties of graphe..." refers background in this paper
...The problem of the bending of graphitic systems and its effect on the hybridization of the π orbitals has been studied a great deal in the context of classical minimal surfaces and applied to fullerenes and carbon nanotubes (Kane and Mele, 1997; Tersoff, 1992; Tu and Ou-Yang, 2002; Xin et al., 2000; Zhong-can et al., 1997)....
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Book•
05 Nov 2012
TL;DR: In this article, Yildirim, O. Zhou, J.E. Fischer, and Nunez-Regueiro studied the electronic properties of Fullerenes.
Abstract: Preface by the Editor. Preface by Sir Harold Kroto. 1. Production of Fullerenes W. Kratschmer. 2. Intercalation Compounds of Fullerenes I: Synthesis, Characterization, and Solid State Properties T. Yildirim, O. Zhou, J.E. Fischer. 3. Intercalation Compounds of Fullerenes II: Structure and Superconductivity of Alkali Metal Fullerides T. Yildirim, O. Zhou, J.E. Fischer. 4. Experimental Studies of the Electronic Structure of Fullerenes M. Knupfer, T. Pichler, M.S. Golden, J. Fink. 5. Polymer and Dimer Phases in Doped Fullerenes K. Prassides. 6. Vibrational Properties of Fullerenes and Fullerides H. Kuzmany, J. Winter. 7. Intercalation Compounds of Fullerenes III: Other Fullerides and Intercalated Nanotubes T. Yildirim, O. Zhou, J.E. Fischer. 8. Structural and Electronic Properties of C60 and C60 Derivatives in the Solid Phases: Calculations Based on Density-Functional Theory W. Andreoni, P. Giannozzi. 9. Carbon Nanotubes M.S. Dresselhaus, G. Dresselhaus, P.C. Eklund, A.M. Rao. 10. Electronic Structure of Carbon and Boron-Carbon-Nitrogen Nanotubes S.G. Louie. 11. Pressure Studies on Fullerenes M. Nunez-Regueiro, L. Marques, J.-L. Hodeau. Index of Materials.
126 citations
TL;DR: In this paper, the energy spectrum of a tight-binding honeycomb lattice in the presence of a uniform magnetic field is analyzed and the graph of the spectrum over a wide range of rational reduced flux Φ/Φ 0 through elementary hexagonal cells is plotted.
Abstract: The energy spectrum of a tight-binding honeycomb lattice in the presence of a uniform magnetic field is analysed. The graph of the spectrum over a wide range of rational reduced flux Φ/Φ 0 through elementary hexagonal cells is plotted. The energy spectrum is found to have recursive properties similar to those discussed previously on the square and triangular lattices. New features of the spectrum are also obtained. Specific properties (gaps, subbands, etc.) are shown to be a direct consequence of frustration and are compared with the spectrum of Bravais lattices. Our results are shown to be relevant for the recent measurements of the upper critical field of a superconducting honeycomb network. A comparison of the structure of the edge of the spectrum on square, triangular and honeycomb lattices is also outlined Analyse du spectre d'energie du modele des liaisons fortes, sur un reseau en nid d'abeilles, en presence d'un champ magnetique uniforme. Etude du graphe du spectre pour differents flux reduits rationnels a travers les cellules elementaires: ce spectre possede des proprietes recursives analogues a celles des reseaux carre et triangulaire. Attribution des proprietes specifiques (bandes interdites, sous-bandes, etc.) a une propriete de frustration; comparaison a celles de reseaux de Bravais
125 citations
Additional excerpts
...Theeigenproblem an be rewritten in terms of Harper's equa-tions (Harper, 1955), and for zigzag edges we obtain (Rammal, 1985):Eµ,kα(k, n) = −t[eika/22 cos(π Φ Φ0 n− ka 2 )β(k, n) + β(k, n− 1)], (114) Eµ,kβ(k, n) = −t[e−ika/22 cos(π Φ Φ0 n− ka 2 )α(k, n) + α(k, n+ 1)], (115) 22 0 1 2 3 4 5 6 7 -1…...
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