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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Journal Article•
TL;DR: The transport properties, which are closely related to those of carbon nanotubes, are dominated by the single epitaxial graphene layer at the silicon carbide interface and reveal the Dirac nature of the charge carriers.
Abstract: Ultrathin epitaxial graphite was grown on single-crystal silicon carbide by vacuum graphitization. The material can be patterned using standard nanolithography methods. The transport properties, which are closely related to those of carbon nanotubes, are dominated by the single epitaxial graphene layer at the silicon carbide interface and reveal the Dirac nature of the charge carriers. Patterned structures show quantum confinement of electrons and phase coherence lengths beyond 1 micrometer at 4 kelvin, with mobilities exceeding 2.5 square meters per volt-second. All-graphene electronically coherent devices and device architectures are envisaged.
4,578 citations
"The electronic properties of graphe..." refers background or result in this paper
...Epitaxially grown multilayers exhibit SdH oscillations with a Berry phase shift of π (Berger et al., 2006), which is the same as the phase shift for Dirac fermions...
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...Epi-taxially grown multilayers exhibit SdH os illations witha Berry phase shift of π (Berger et al., 2006), whi his the same as the phase shift for Dira fermions ob-served in a single layer as well as for some subbandspresent in multilayer graphene (see further) and graphite(Luk'yan huk and…...
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...…grown this way is heavily doped due to the harge transfer from the substrate to the graphene layer(with the hemi al potential well above the Dira point)and therefore all samples have strong metalli hara -ter with large ele troni mobilities (Berger et al., 2006;de Heer et al., 2007)....
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...Moreover, graphene grown this way is heavily doped due to the charge transfer from the substrate to the graphene layer (with the chemical potential well above the Dirac point) and therefore all samples have strong metallic character with large electronic mobilities (Berger et al., 2006; de Heer et al., 2007)....
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TL;DR: In this paper, the authors present a theoretical study of soliton formation in long-chain polyenes, including the energy of formation, length, mass, and activation energy for motion.
Abstract: We present a theoretical study of soliton formation in long-chain polyenes, including the energy of formation, length, mass, and activation energy for motion. The results provide an explanation of the mobile neutral defect observed in undoped ${(\mathrm{CH})}_{x}$. Since the soliton formation energy is less than that needed to create band excitation, solitons play a fundamental role in the charge-transfer doping mechanism.
4,562 citations
"The electronic properties of graphe..." refers background in this paper
...…and, as in the Figure 12 (Color online) Sket h of the three inequivalent ori-entations of graphene layers with respe t to ea h other. ase of other arbon based systems su h as polya ethy-lene (Su et al., 1979, 1980), it an lead to soliton-likeex itations (Hou et al., 2007; Ja kiw and Rebbi, 1976)....
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TL;DR: The authors' ab initio calculations show that the origin of energy gaps for GNRs with armchair shaped edges arises from both quantum confinement and the crucial effect of the edges, which differs from the results of simple tight-binding calculations or solutions of the Dirac's equation based on them.
Abstract: Based on a first-principles approach, we present scaling rules for the band gaps of graphene nanoribbons (GNRs) as a function of their widths. The GNRs considered have either armchair or zigzag shaped edges on both sides with hydrogen passivation. Both varieties of ribbons are shown to have band gaps. This differs from the results of simple tight-binding calculations or solutions of the Dirac's equation based on them. Our ab initio calculations show that the origin of energy gaps for GNRs with armchair shaped edges arises from both quantum confinement and the crucial effect of the edges. For GNRs with zigzag shaped edges, gaps appear because of a staggered sublattice potential on the hexagonal lattice due to edge magnetization. The rich gap structure for ribbons with armchair shaped edges is further obtained analytically including edge effects. These results reproduce our ab initio calculation results very well.
4,471 citations
"The electronic properties of graphe..." refers background in this paper
...More detailedab initio al ulations of the spe tra of graphene nanorib-bons show that intera tion e e ts an lead to ele troni gaps (Son et al., 2006b) and magneti states lose to thegraphene edges, independent of their nature (Son et al.,2006a; Yang et al., 2007a,b)....
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TL;DR: In this paper, the structure of the electronic energy bands and Brillouin zones for graphite was developed using the "tight binding" approximation, and it was found that graphite is a semi-conductor with zero activation energy, but they are created at higher temperatures by excitation to a band contiguous to the highest one which is normally filled.
Abstract: The structure of the electronic energy bands and Brillouin zones for graphite is developed using the "tight binding" approximation. Graphite is found to be a semi-conductor with zero activation energy, i.e., there are no free electrons at zero temperature, but they are created at higher temperatures by excitation to a band contiguous to the highest one which is normally filled. The electrical conductivity is treated with assumptions about the mean free path. It is found to be about 100 times as great parallel to as across crystal planes. A large and anisotropic diamagnetic susceptibility is predicted for the conduction electrons; this is greatest for fields across the layers. The volume optical absorption is accounted for.
4,395 citations
"The electronic properties of graphe..." refers background or methods or result in this paper
...unusual semimetallic behavior in this material (Wallace, 1947)....
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...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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...This result was first obtained by Wallace (Wallace, 1947)....
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...The energy bands derived from this Hamiltonian have the form (Wallace, 1947):...
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...(3), as: k = K+q, with |q| |K| (Wallace, 1947):...
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TL;DR: In this article, a review of the progress made in the last several years in understanding the properties of disordered electronic systems is presented, focusing on the metal-to-insulator transition and problems associated with the insulator.
Abstract: This paper reviews the progress made in the last several years in understanding the properties of disordered electronic systems. Even in the metallic limit, serious deviations from the Boltzmann transport theory and Fermi-liquid theory have been predicted and observed experimentally. There are two important ingredients in this new understanding: the concept of Anderson localization and the effects of interaction between electrons in a disordered medium. This paper emphasizes the theoretical aspect, even though some of the relevant experiments are also examined. The bulk of the paper focuses on the metallic side, but the authors also discuss the metal-to-insulator transition and comment on problems associated with the insulator.
4,095 citations
"The electronic properties of graphe..." refers background in this paper
...Infa t, under ertain onditions, Dira fermions are im-mune to lo alization e e ts observed in ordinary ele -trons (Lee and Ramakrishnan, 1985) and it has been es-tablished experimentally that ele trons an propagatewithout s attering over large distan es of the order ofmi rometers in graphene…...
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