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: This work investigates the minimum conductivity of graphene within a quasiclassical approach taking into account electron-hole coherence effects which stem from the chiral nature of low energy excitations and studies both the electrical and the thermal conductivity whose relation satisfies the Wiedemann-Franz law.
Abstract: We investigate the minimum conductivity of graphene within a quasiclassical approach taking into account electron-hole coherence effects which stem from the chiral nature of low energy excitations. Relying on an analytical solution of the kinetic equation in the electron-hole coherent and incoherent cases, we study both the electrical and the thermal conductivity whose relation satisfies the Wiedemann-Franz law. We find that most of the previous findings based on the Boltzmann equation are restricted to only high mobility samples where electron-hole coherence effects are not sufficient.
88 citations
TL;DR: A theory for recent STM studies of Zn impurities in the superconductor Bi2Sr2CaCu2O8+delta is presented, arguing that the Kondo spin dynamics of this moment is the origin of the low bias peak in the differential conductance, rather than a resonance in a purely potential scattering model.
Abstract: We present a theory for recent STM studies of Zn impurities in the superconductor ${\mathrm{Bi}}_{2}{\mathrm{Sr}}_{2}{\mathrm{CaCu}}_{2}{\mathrm{O}}_{8+\ensuremath{\delta}}$, using insights from NMR experiments which show that there is a net $S\phantom{\rule{0ex}{0ex}}=\phantom{\rule{0ex}{0ex}}1/2$ moment on the Cu ions near the Zn. We argue that the Kondo spin dynamics of this moment is the origin of the low bias peak in the differential conductance, rather than a resonance in a purely potential scattering model. The spatial and energy dependence of the STM spectra of our model can also fit the experiments.
88 citations
"The electronic properties of graphe..." refers background in this paper
...…state is not formed unless the ex hange ouplingex eeds a riti al value, of the order of the ele tronbandwidth, a problem already studied in onne tionwith magneti impurities in d-wave super ondu tors(Cassanello and Fradkin, 1996, 1997; Fritz et al., 2006;Polkovnikov, 2002; Polkovnikov et al., 2001)....
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TL;DR: In this paper, it was shown that identical transport properties arise when the doped graphitic leads are replaced by quantum wires and that the duality between graphitic and metallic leads originates in the selection of modes with transverse momentum close to the $K$ points, and can be extended to a wide class of contact models.
Abstract: Recent investigations address transport through ballistic charge-neutral graphene strips coupled to doped graphitic leads. This paper shows that identical transport properties arise when the leads are replaced by quantum wires. This duality between graphitic and metallic leads originates in the selection of modes with transverse momentum close to the $K$ points, and can be extended to a wide class of contact models. Among this class, we identify a simple, effective contact model, which provides an efficient tool to study the transport through extended weakly-doped graphitic systems.
87 citations
TL;DR: This work discusses, for a two-dimensional Dirac Hamiltonian with a random scalar potential, the presence of a Z2 topological term in the nonlinear sigma model encoding the physics of Anderson localization in the symplectic symmetry class.
Abstract: We discuss, for a two-dimensional Dirac Hamiltonian with a random scalar potential, the presence of a ${\mathbb{Z}}_{2}$ topological term in the nonlinear sigma model encoding the physics of Anderson localization in the symplectic symmetry class. The ${\mathbb{Z}}_{2}$ topological term realizes the sign of the Pfaffian of a family of Dirac operators. We compute the corresponding global anomaly, i.e., the change in the sign of the Pfaffian by studying a spectral flow numerically. This ${\mathbb{Z}}_{2}$ topological effect can be relevant to graphene when the impurity potential is long ranged and, also, to the two-dimensional boundaries of a three-dimensional lattice model of ${\mathbb{Z}}_{2}$ topological insulators in the symplectic symmetry class.
87 citations
"The electronic properties of graphe..." refers background in this paper
...This result is valid when intervalley s attering is ne-gle ted (Ostrovsky et al., 2006, 2007; Ryu et al., 2007)....
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TL;DR: In this article, a microscopic random-phase-approximation theory was used to analyze the properties of a chiral two-dimensional electron gas in density-functional-theory applications to graphene nanostructures.
87 citations
"The electronic properties of graphe..." refers background in this paper
...…tron transistor (SET) show very littlesign of intera tions in the system, being well ttedby the non-intera ting result that, ontrary to thetwo-dimensional ele tron gas (2DEG) (Eisenstein et al.,1994; Giuliani and Vignale, 2005), is positively diver-gent (Martin et al., 2007; Polini et al., 2007)....
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