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
References
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TL;DR: In this article, the electronic spectrum of sheets of graphite (plane honeycomb lattice) folded into regular polyhedra is studied and a continuum limit valid for sufficiently large molecules and based on the tight-binding approximation is derived.
250 citations
"The electronic properties of graphe..." refers background in this paper
...Far away from the defe t, a slow rotation of the omponents of the spinorial wavefun tion an be de-s ribed by a gauge eld whi h a ts on the valleyand sublatti e indi es (González et al., 1992, 1993b)....
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...The nal ontinuum equation gives a reasonable des rip-tion of the ele troni spe trum of fullerenes of di er-ent sizes (González et al., 1992, 1993b), and other stru -tures whi h ontain pentagons (Kolesnikov and Osipov,2004, 2006; Lammert and Crespi, 2004; LeClair, 2000;Osipov et al., 2003)....
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...This gauge eld is te hni ally non-abelian, althougha transformation an be de ned whi h makes the re-sulting Dira equation equivalent to one with an e e -tive abelian gauge eld (González et al., 1993b)....
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...In the random phase approxima-tion (RPA), the polarization fun tion an be al ulatedanalyti ally (González et al., 1993a, 1994; Shung, 1986a): Π(q, ω) = q2 4 √ v2F q 2 − ω2 , (215)and hen e, for ω > vF q the polarization fun tion is imag-inary indi ating the damping of ele tron-hole pairs....
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TL;DR: In this paper, it was shown that tunnelling without exponential suppression occurs when an electron is incident on a high barrier, even when the barrier is not high enough to radiate.
Abstract: The early papers by Klein, Sauter and Hund which investigate scattering off a high step potential in the context of the Dirac equation are discussed to derive the 'paradox' first obtained by Klein. The explanation of this effect in terms of electron-positron production is re-assessed. It is shown that a potential well or barrier in the Dirac equation can become supercritical and emit positrons or electrons spontaneously if the potential is strong enough. If the well or barrier is wide enough, a seemingly constant current is emitted. This phenomenon is transient whereas the tunnelling first calculated by Klein is time-independent. It is shown that tunnelling without exponential suppression occurs when an electron is incident on a high barrier, even when the barrier is not high enough to radiate. Klein tunnelling is therefore a property of relativistic wave equations and is not necessarily connected to particle emission. The Coulomb potential is investigated and it is shown that a heavy nucleus of sufficien...
249 citations
"The electronic properties of graphe..." refers background in this paper
...Another particularly interesting feature of Dirac fermions is their insensitivity to external electrostatic potentials due to the so-called Klein paradox, that is, the fact that Dirac fermions can be transmitted with probability one through a classically forbidden region (Calogeracos and Dombey, 1999; Itzykson and Zuber, 2006)....
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...paradox (Calogeracos and Dombey, 1999; Itzykson and Zuber, 2006) and does not occur for non-relativistic electrons....
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TL;DR: This work explains the observed conductance quantization, which is fractional in the bipolar regime and an integer in the unipolar regime, in terms of quantum Hall edge modes propagating along and across the p-n interface.
Abstract: Recent experimental work on locally gated graphene layers resulting in p-n junctions has revealed the quantum Hall effect in their transport behavior. We explain the observed conductance quantization, which is fractional in the bipolar regime and an integer in the unipolar regime, in terms of quantum Hall edge modes propagating along and across the p-n interface. In the bipolar regime, the electron and hole modes can mix at the p-n boundary, leading to current partition and quantized shot-noise plateaus similar to those of conductance, whereas in the unipolar regime transport is noiseless. These quantum Hall phenomena reflect the massless Dirac character of charge carriers in graphene, with particle/hole interplay manifest in mode mixing and noise in the bipolar regime.
248 citations
"The electronic properties of graphe..." refers background in this paper
...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)....
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...At the jun tion, hiral urrents an ow at both edges (Abanin and Levitov, 2007), indu ing ba ks atter-ing between the Hall urrents at the edges of the sample....
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TL;DR: In this article, the authors investigate experimentally transport through ring-shaped devices etched in graphene and observe clear Aharonov-Bohm conductance oscillations, and observe an unexpected linear dependence of the oscillation amplitude on the ring conductance.
Abstract: We investigate experimentally transport through ring-shaped devices etched in graphene and observe clear Aharonov-Bohm conductance oscillations. The temperature dependence of the oscillation amplitude indicates that below 1 K, the phase coherence length is comparable to or larger than the size of the ring. An increase in the amplitude is observed at high magnetic field, when the cyclotron diameter becomes comparable to the width of the arms of the ring. By measuring the dependence on gate voltage, we find that the Aharonov-Bohm effect vanishes at the charge neutrality point, and we observe an unexpected linear dependence of the oscillation amplitude on the ring conductance.
246 citations
TL;DR: In this article, the Dirac equation was used to determine the maximal supercurrent that can flow through an undoped strip of graphene with heavily doped superconducting electrodes, and the result was shown to be the same as in this paper.
Abstract: We solve the Dirac\char21{}Bogoliubov\char21{}de Gennes equation in an impurity-free superconductor\char21{}normal-metal\char21{}superconductor junction, to determine the maximal supercurrent ${I}_{c}$ that can flow through an undoped strip of graphene with heavily doped superconducting electrodes. The result ${I}_{c}\ensuremath{\simeq}(W∕L)e{\ensuremath{\Delta}}_{0}∕\ensuremath{\hbar}$ is determined by the superconducting gap ${\ensuremath{\Delta}}_{0}$ and by the aspect ratio of the junction (length $L$ small relative to the width $W$ and to the superconducting coherence length). Moving away from the Dirac point of zero doping, we recover the usual ballistic result ${I}_{c}\ensuremath{\simeq}(W∕{\ensuremath{\lambda}}_{F})e{\ensuremath{\Delta}}_{0}∕\ensuremath{\hbar}$, in which the Fermi wavelength ${\ensuremath{\lambda}}_{F}$ takes over from $L$. The product ${I}_{c}{R}_{\mathrm{N}}\ensuremath{\simeq}{\ensuremath{\Delta}}_{0}∕e$ of the critical current and normal-state resistance retains its universal value (up to a numerical prefactor) on approaching the Dirac point.
245 citations
"The electronic properties of graphe..." refers background in this paper
...The scattering of electrons near the Dirac point by graphene-superconductor junctions differs from Andreev scattering process in normal metals (Titov and Beenakker, 2006)....
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...The s attering of ele trons near the Dira pointby graphene-super ondu tor jun tions di ers fromAndreev s attering pro ess in normal metals(Titov and Beenakker, 2006)....
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