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 demonstrates the controlled induction of an insulating state--with large suppression of the conductivity--in bilayer graphene, by using a double-gate device configuration that enables an electric field to be applied perpendicular to the plane.
Abstract: The potential of graphene-based materials consisting of one or a few layers of graphite for integrated electronics originates from the large room-temperature carrier mobility in these systems (approximately 10,000 cm2 V(-1) s(-1)). However, the realization of electronic devices such as field-effect transistors will require controlling and even switching off the electrical conductivity by means of gate electrodes, which is made difficult by the absence of a bandgap in the intrinsic material. Here, we demonstrate the controlled induction of an insulating state--with large suppression of the conductivity--in bilayer graphene, by using a double-gate device configuration that enables an electric field to be applied perpendicular to the plane. The dependence of the resistance on temperature and electric field, and the absence of any effect in a single-layer device, strongly suggest that the gate-induced insulating state originates from the recently predicted opening of a bandgap between valence and conduction bands.
1,495 citations
"The electronic properties of graphe..." refers background in this paper
...…most versatile systems in ondensedmatter resear h.Besides the unusual basi properties, graphene hasthe potential for a large number of appli ations(Geim and Novoselov, 2007), from hemi al sensors(Chen et al., 2007 ; S hedin et al., 2007) to transistors(Nilsson et al., 2007b; Oostinga et al., 2007)....
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TL;DR: In this paper, the authors studied the visibility of graphene and showed that it depends strongly on both thickness of silicon dioxide and light wavelength, and they used a Fresnel-law-based model to quantitatively describe the experimental data without any fitting parameters.
Abstract: Microfabrication of graphene devices used in many experimental studies currently relies on the fact that graphene crystallites can be visualized using optical microscopy if prepared on top of silicon wafers with a certain thickness of silicon dioxide. We study graphene's visibility and show that it depends strongly on both thickness of silicon dioxide and light wavelength. We have found that by using monochromatic illumination, graphene can be isolated for any silicon dioxide thickness, albeit 300 nm (the current standard) and, especially, approx. 100 nm are most suitable for its visual detection. By using a Fresnel-law-based model, we quantitatively describe the experimental data without any fitting parameters.
1,487 citations
"The electronic properties of graphe..." refers background in this paper
..., 2004) that allows its observation with an ordinary optical microscope (Abergel et al., 2007; Blake et al., 2007; Casiraghi et al., 2007)....
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...Graphene was even-tually spotted due to the subtle opti al e e t it reates ontop of a leverly hosen SiO2 substrate (Novoselov et al.,2004) that allows its observation with an ordinary opti- al mi ros ope (Abergel et al., 2007; Blake et al., 2007;Casiraghi et al., 2007)....
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TL;DR: In this article, the wave vector dependent plasmon dispersion and the static screening function of the Coulomb interaction in 2D graphene layer were found in the self-consistent field approximation.
Abstract: The dynamical dielectric function of two dimensional graphene at arbitrary wave vector $q$ and frequency $\omega$, $\epsilon(q,\omega)$, is calculated in the self-consistent field approximation. The results are used to find the dispersion of the plasmon mode and the electrostatic screening of the Coulomb interaction in 2D graphene layer within the random phase approximation. At long wavelengths ($q\to 0$) the plasmon dispersion shows the local classical behavior $\omega_{cl} = \omega_0 \sqrt{q}$, but the density dependence of the plasma frequency ($\omega_0 \propto n^{1/4}$) is different from the usual 2D electron system ($\omega_0 \propto n^{1/2}$). The wave vector dependent plasmon dispersion and the static screening function show very different behavior than the usual 2D case.
1,483 citations
TL;DR: In this article, a scanning single-electron transistor is used to map the local density of states and the carrier density landscape in the vicinity of the neutrality point, and it is shown that electron-hole puddles can be quantitatively accounted for by considering noninteracting electrons and holes.
Abstract: The electronic structure of graphene causes its charge carriers to behave like relativistic particles. For a perfect graphene sheet free from impurities and disorder, the Fermi energy lies at the so-called ‘Dirac point’, where the density of electronic states vanishes. But in the inevitable presence of disorder, theory predicts that equally probable regions of electron-rich and hole-rich puddles will arise. These puddles could explain graphene’s anomalous non-zero minimal conductivity at zero average carrier density. Here, we use a scanning single-electron transistor to map the local density of states and the carrier density landscape in the vicinity of the neutrality point. Our results confirm the existence of electron–hole puddles, and rule out extrinsic substrate effects as explanations for their emergence and topology. Moreover, we find that, unlike non-relativistic particles the density of states can be quantitatively accounted for by considering non-interacting electrons and holes.
1,464 citations
"The electronic properties of graphe..." refers background in this paper
...Single ele -tron transistor (SET) measurements of graphene showthat this seems to be the situation in graphene at half- lling (Martin et al., 2007)....
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...…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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...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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TL;DR: In this paper, the physics of weak localization is discussed and the experimental results as well as the theory is reviewed, and the role of spin-orbit scattering and the magnetic scattering are discussed.
1,439 citations