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: It is found that a non-negligible edge state survives even in graphene ribbons with less developed zigzag edges, when the system size is on a nanometer scale.
Abstract: Finite graphite systems having a zigzag edge exhibit a special edge state. The corresponding energy bands are almost flat at the Fermi level and thereby give a sharp peak in the density of states. The charge density in the edge state is strongly localized on the zigzag edge sites. No such localized state appears in graphite systems having an armchair edge. By utilizing the graphene ribbon model, we discuss the effect of the system size and edge shape on the special edge state. By varying the width of the graphene ribbons, we find that the nanometer size effect is crucial for determining the relative importance of the edge state. We also have extended the graphene ribbon to have edges of a general shape, which is defined as a mixture of zigzag and armchair sites. Examining the relative importance of the edge state for graphene ribbons with general edges, we find that a non-negligible edge state survives even in graphene ribbons with less developed zigzag edges. We demonstrate that such an edge shape with three or four zigzag sites per sequence is sufficient to show an edge state, when the system size is on a nanometer scale. The special characteristics of the edge state play a large role in determining the density of states near the Fermi level for graphite networks on a nanometer scale.
3,834 citations
"The electronic properties of graphe..." refers background or methods in this paper
...This was originally done both with and without a magnetic field (Brey and Fertig, 2006a,b; Nakada et al., 1996)....
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...This was originally done both with and without amagneti eld (Brey and Fertig, 2006a,b; Nakada et al.,1996).1....
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...sity of states (Nakada et al., 1996) that can be probed by Raman spectroscopy....
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...Hen e, lean nanorib-bons must have 1D square root singularities in their den-sity of states (Nakada et al., 1996) that an be probedby Raman spe tros opy....
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...The spe trum of graphene nanoribbonsThe spe trum of graphene nanoribbons depend verymu h on the nature of their edges zigzag or arm hair(Brey and Fertig, 2006a,b; Nakada et al., 1996)....
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TL;DR: In this article, it was shown that if in-plane homogeneous electric fields are applied across the zigzag-shaped edges of the graphene nanoribbons, their magnetic properties can be controlled by the external electric fields.
Abstract: Electrical current can be completely spin polarized in a class of materials known as half-metals, as a result of the coexistence of metallic nature for electrons with one spin orientation and insulating nature for electrons with the other. Such asymmetric electronic states for the different spins have been predicted for some ferromagnetic metals--for example, the Heusler compounds--and were first observed in a manganese perovskite. In view of the potential for use of this property in realizing spin-based electronics, substantial efforts have been made to search for half-metallic materials. However, organic materials have hardly been investigated in this context even though carbon-based nanostructures hold significant promise for future electronic devices. Here we predict half-metallicity in nanometre-scale graphene ribbons by using first-principles calculations. We show that this phenomenon is realizable if in-plane homogeneous electric fields are applied across the zigzag-shaped edges of the graphene nanoribbons, and that their magnetic properties can be controlled by the external electric fields. The results are not only of scientific interest in the interplay between electric fields and electronic spin degree of freedom in solids but may also open a new path to explore spintronics at the nanometre scale, based on graphene.
3,519 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, it was shown that the Klein paradox can be tested in a conceptually simple condensed-matter experiment using electrostatic barriers in single and bi-layer graphene, showing that quantum tunnelling in these materials becomes highly anisotropic, qualitatively different from the case of normal, non-relativistic electrons.
Abstract: The so-called Klein paradox—unimpeded penetration of relativistic particles through high and wide potential barriers—is one of the most exotic and counterintuitive consequences of quantum electrodynamics. The phenomenon is discussed in many contexts in particle, nuclear and astro-physics but direct tests of the Klein paradox using elementary particles have so far proved impossible. Here we show that the effect can be tested in a conceptually simple condensed-matter experiment using electrostatic barriers in single- and bi-layer graphene. Owing to the chiral nature of their quasiparticles, quantum tunnelling in these materials becomes highly anisotropic, qualitatively different from the case of normal, non-relativistic electrons. Massless Dirac fermions in graphene allow a close realization of Klein’s gedanken experiment, whereas massive chiral fermions in bilayer graphene offer an interesting complementary system that elucidates the basic physics involved.
3,402 citations
"The electronic properties of graphe..." refers background or methods in this paper
...(179) The transmission at normal in iden e, ky = 0, is one,in agreement with the absen e of ba ks attering ingraphene, for any barrier that does not indu e intervalleys attering (Katsnelson et al., 2006)....
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...When intervalley s at-tering and the la k of symmetry between sublatti es arenegle ted, a potential barrier shows no re e tion for ele -trons in ident in the normal dire tion (Katsnelson et al.,2006)....
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...Finally,at half- lling, due to disorder graphene an be dividedin ele tron and hole harge puddles (Katsnelson et al.,2006; Martin et al., 2007)....
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...Chiral Tunneling and Klein paradoxIn this se tion we want to address the s attering of hiral ele trons in two dimensions by a square barrier(Katsnelson, 2007b; Katsnelson et al., 2006)....
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...…by the fa t thatin graphene the Dira fermions move with a speed vFwhi h is 300 times smaller than the speed of light, c. Hen e, many of the unusual properties of QED an show up in graphene but at mu h smaller speeds(Castro Neto et al., 2006a; Katsnelson and Novoselov,2007; Katsnelson et al., 2006)....
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3,323 citations
TL;DR: In this paper, ultrathin epitaxial graphite films were grown by thermal decomposition on the (0001) surface of 6H−SiC, and characterized by surface science techniques.
Abstract: We have produced ultrathin epitaxial graphite films which show remarkable 2D electron gas (2DEG) behavior. The films, composed of typically three graphene sheets, were grown by thermal decomposition on the (0001) surface of 6H−SiC, and characterized by surface science techniques. The low-temperature conductance spans a range of localization regimes according to the structural state (square resistance 1.5 kΩ to 225 kΩ at 4 K, with positive magnetoconductance). Low-resistance samples show characteristics of weak localization in two dimensions, from which we estimate elastic and inelastic mean free paths. At low field, the Hall resistance is linear up to 4.5 T, which is well-explained by n-type carriers of density 1012 cm-2 per graphene sheet. The most highly ordered sample exhibits Shubnikov−de Haas oscillations that correspond to nonlinearities observed in the Hall resistance, indicating a potential new quantum Hall system. We show that the high-mobility films can be patterned via conventional lithographic...
3,315 citations