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: Comparison with a theoretical model which includes quasiparticle interactions has allowed a determination of the inhomogeneous broadening due to density fluctuations and has provided evidence of a second, apparently distinct, source of disorder.
Abstract: A quantitative study of the compressibility of the two-dimensional electron gas in GaAs heterostrutures is reported. Using a recently developed capacitive technique that avoids the large offset signals characteristic of conventional methods, high-precision compressibility data at both zero and high magnetic field has been obtained. The curious negative sign of the compressibility in certain regimes is shown to be a consequence of electron-electron interactions. Detailed numerical calculations show that the zero-field data are fully consistent with the known exchange energy, provided the finite thickness of the electron gas is properly included. At high magnetic fields, in the extreme quantum limit, the integrated compressibility signal is used to obtain a quantitative measure of the chemical potential discontinuity associated with the nu = 1/3 fractional quantum Hall effect. Comparison with a theoretical model which includes quasiparticle interactions has allowed a determination of the inhomogeneous broadening due to density fluctuations and has provided evidence of a second, apparently distinct, source of disorder. While the origin of this disorder is not fully understood, the data are consistent with simple lifetime broadening of the quasiparticle states.
188 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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TL;DR: It is shown that there is a phase transition between the semimetal and metallic phases followed by a localization transition and the symmetry breaking associated with this transition is related to the nonsymmorphic character of the space group.
Abstract: A model that describes the qualitative properties of the electronic states of a disordered degenerate semiconductor with a finite number of degeneracy points is proposed. I introduce an effective Hamiltonian of the form of a Dirac operator coupled to randomly distributed fields. It is shown that there is a phase transition between the semimetal and metallic phases followed by a localization transition. The symmetry breaking associated with this transition is related to the nonsymmorphic character of the space group. The density of states plays the role of the order parameter and the elastic mean free path is the correlation length. A path-integral representation is introduced and used to characterize the universality class of this transition. The lower critical dimension is 2. A mapping of the two-dimensional case to one-dimensional self-interacting Fermi systems is presented. Applications to zero-gap semiconductors and other systems are discussed.
182 citations
TL;DR: In this article, the presence of ferromagnetic magnetism in the phase diagram of the two-dimensional honeycomb lattice close to half-filling (graphene) as a function of the strength of the Coulomb interaction and doping was studied.
Abstract: We study the presence of ferromagnetism in the phase diagram of the two-dimensional honeycomb lattice close to half-filling (graphene) as a function of the strength of the Coulomb interaction and doping. We show that exchange interactions between Dirac fermions can stabilize a ferromagnetic phase at low doping when the coupling is sufficiently large. In clean systems the zero-temperature phase diagram shows both first-order and second-order transition lines and two distinct ferromagnetic phases: one phase with only one type of carriers (either electrons or holes) and another with two types of carriers (electrons and holes). Using the coherent potential approximation we argue that disorder further stabilizes the ferromagnetic phase. This work should estimulate Monte Carlo calculations in graphene dealing with the long-range nature of the Coulomb potencial.
182 citations
"The electronic properties of graphe..." refers background in this paper
...This result indi ates that strongly orrelated ele -troni phases, su h as ferromagnetism (Peres et al., 2005)and Wigner rystals (Dahal et al., 2006) are suppressedin lean graphene....
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...Itwas shown previously that the ex hange ontribution tothe ele troni energy of a single graphene layer does notlead to a ferromagneti instability (Peres et al., 2005)....
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TL;DR: In this article, the electron-electron interaction induced many-body effects in undoped and doped two-dimensional (2D) graphene layers and showed that intrinsic graphene is a marginal Fermi liquid with the imaginary part of the self-energy varying linearly in energy.
Abstract: We consider theoretically the electron-electron interaction induced many-body effects in undoped (``intrinsic'') and doped (``extrinsic'') two-dimensional (2D) graphene layers We find that (1) intrinsic graphene is a marginal Fermi liquid with the imaginary part of the self-energy, $\mathrm{Im}\phantom{\rule{02em}{0ex}}\ensuremath{\Sigma}(\ensuremath{\omega})$, varying linearly in energy $\ensuremath{\omega}$ for small $\ensuremath{\omega}$, implying that the quasiparticle spectral weight vanishes at the Dirac point as ${(\mathrm{ln}\phantom{\rule{02em}{0ex}}\ensuremath{\omega})}^{\ensuremath{-}1}$; and (2) extrinsic graphene is a well-defined Fermi liquid with $\mathrm{Im}\phantom{\rule{02em}{0ex}}\ensuremath{\Sigma}(\ensuremath{\omega})\ensuremath{\sim}{\ensuremath{\omega}}^{2}\phantom{\rule{02em}{0ex}}\mathrm{ln}\phantom{\rule{02em}{0ex}}\ensuremath{\omega}$ near the Fermi surface similar to 2D carrier systems with parabolic energy dispersion We provide analytical and numerical results for quasiparticle renormalization in graphene, concluding that all experimental graphene systems are ordinary 2D Fermi liquids since any doping automatically induces generic Fermi liquid behavior
182 citations
"The electronic properties of graphe..." refers background in this paper
...The stati diele tri onstant has a ontinuous derivative at 2kF, unlike in the ase of the 2D ele tron gas (Ando, 2006b; Sarma et al.,2007; Wuns h et al., 2006)....
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...Thesimpli ity of the band stru ture of graphene allows an-alyti al al ulation of the energy and momentum de-penden e of the diele tri fun tion (Sarma et al., 2007;Wuns h et al., 2006)....
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TL;DR: Magnetotransport measurements performed on several well-characterized highly oriented pyrolitic graphite and single crystalline Kish graphite samples reveal a reentrant metallic behavior in the basal-plane resistance at high magnetic fields, when only the lowest Landau levels are occupied.
Abstract: Magnetotransport measurements performed on several well-characterized highly oriented pyrolitic graphite and single crystalline Kish graphite samples reveal a reentrant metallic behavior in the basal-plane resistance at high magnetic fields, when only the lowest Landau levels are occupied. The results suggest that the quantum Hall effect and Landau-level-quantization-induced superconducting correlations are relevant to understand the metalliclike state(s) in graphite in the quantum limit.
180 citations