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: It is shown here that the transistors exhibit two different kinds of hysteresis in their electrical characteristics, and it is found that an ice layer on/under graphene has a much stronger dipole moment than a water layer does.
Abstract: Graphene field effect transistors commonly comprise graphene flakes lying on SiO2 surfaces. The gate-voltage dependent conductance shows hysteresis depending on the gate sweeping rate/range. It is shown here that the transistors exhibit two different kinds of hysteresis in their electrical characteristics. Charge transfer causes a positive shift in the gate voltage of the minimum conductance, while capacitive gating can cause the negative shift of conductance with respect to gate voltage. The positive hysteretic phenomena decay with an increase of the number of layers in graphene flakes. Self-heating in a helium atmosphere significantly removes adsorbates and reduces positive hysteresis. We also observed negative hysteresis in graphene devices at low temperature. It is also found that an ice layer on/under graphene has a much stronger dipole moment than a water layer does. Mobile ions in the electrolyte gate and a polarity switch in the ferroelectric gate could also cause negative hysteresis in graphene t...
593 citations
Cites background from "The electronic properties of graphe..."
...accessible and links solid state devices to molecular electronics.(2,3) Graphene is identi-...
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TL;DR: In this article, the structural, vibrational and electronic properties of the monolayer graphene-like transition-metal dichalcogenide (MX2) sheets were investigated using first principles calculations.
Abstract: Using first principles calculations, we investigate the structural, vibrational and electronic structures of the monolayer graphene-like transition-metal dichalcogenide (MX2) sheets. We find the lattice parameters and stabilities of the MX2 sheets are mainly determined by the chalcogen atoms, while the electronic properties depend on the metal atoms. The NbS2 and TaS2 sheets have comparable energetic stabilities to the synthesized MoS2 and WS2 ones. The molybdenum and tungsten dichalcogenide (MoX2 and WX2) sheets have similar lattice parameters, vibrational modes, and electronic structures. These analogies also exist between the niobium and tantalum dichalcogenide (NbX2 and TaX2) sheets. However, the NbX2 and TaX2 sheets are metals, while the MoX2 and WX2 ones are semiconductors with direct-band gaps. When the Nb and Ta atoms are doped into the MoS2 and WS2 sheets, a semiconductor-to-metal transition occurs. Comparing to the bulk compounds, these monolayer sheets have similar structural parameters and properties, but their vibrational and electronic properties are varied and have special characteristics. Our results suggest that the graphene-like MX2 sheets have potential applications in nano-electronics and nano-devices.
593 citations
TL;DR: In this article, the band structure of a two-dimensional honeycomb lattice of silicon atoms is investigated and the authors show that the gap closes at a certain critical electric field, and that it is possible to generate helical zero modes anywhere in a silicene sheet by adjusting the electric field.
Abstract: Silicene is a monolayer of silicon atoms forming a two-dimensional honeycomb lattice, which shares almost every remarkable property with graphene. The low energy structure of silicene is described by Dirac electrons with relatively large spin-orbit interactions due to its buckled structure. The key observation is that the band structure is controllable by applying the electric field to a silicene sheet. In particular, the gap closes at a certain critical electric field. Examining the band structure of a silicene nanoribbon, we demonstrate that a topological phase transition occurs from a topological insulator to a band insulator with the increase of the electric field. We also show that it is possible to generate helical zero modes anywhere in a silicene sheet by adjusting the electric field locally to this critical value. The region may act as a quantum wire or a quantum dot surrounded by topological and/or band insulators. We explicitly construct the wave functions for some simple geometries based on the low-energy effective Dirac theory. These results are applicable also to germanene, that is a two-dimensional honeycomb structure of germanium.
593 citations
TL;DR: This work reports the emergence of Dirac fermions in a fully tunable condensed-matter system—molecular graphene—assembled by atomic manipulation of carbon monoxide molecules over a conventional two-dimensional electron system at a copper surface and shows the existence within the system of linearly dispersing, massless quasi-particles accompanied by a density of states characteristic of graphene.
Abstract: The formation of massless Dirac fermions is demonstrated in a highly tunable molecular graphene lattice, and particular distortions of the lattice are shown to endow the fermions with mass or engage the fermions with artificial electric and magnetic fields. The electronic structure of certain solids causes them to exhibit 'Dirac points', which lie at the heart of many fascinating phenomena in condensed-matter physics. In graphene, for example, they cause electrons to act as massless Dirac fermions, able to travel at the speed of light. Two very different methods for controlling the properties of Dirac fermions are presented in this issue of Nature. In conventional solids, the electronic structure of the material cannot be varied, so it is difficult to see how the properties of Dirac fermions could be controlled. To avoid this constraint, Tarruell et al. create a tunable system of ultracold quantum gases within an adjustable honeycomb optical lattice. This model simulates condensed-matter physics, with atoms in the role of electrons. The Dirac points can be moved and merged to explore the physics of exotic materials such as topological insulators and graphene. Gomes et al. describe a more direct approach, creating an artificial form of molecular graphene by arranging carbon monoxide molecules, with atomic precision, in a honeycomb pattern on top of a two-dimensional electron system. Lattice parameters are adjustable, allowing the study of the properties of Dirac electrons and even the production of 'pseudo' electric and magnetic fields. This work highlights an innovative technique for constructing artificial materials with molecular assembly, including designer Dirac materials harbouring new ground states. The observation of massless Dirac fermions in monolayer graphene has generated a new area of science and technology seeking to harness charge carriers that behave relativistically within solid-state materials1. Both massless and massive Dirac fermions have been studied and proposed in a growing class of Dirac materials that includes bilayer graphene, surface states of topological insulators and iron-based high-temperature superconductors. Because the accessibility of this physics is predicated on the synthesis of new materials, the quest for Dirac quasi-particles has expanded to artificial systems such as lattices comprising ultracold atoms2,3,4. Here we report the emergence of Dirac fermions in a fully tunable condensed-matter system—molecular graphene—assembled by atomic manipulation of carbon monoxide molecules over a conventional two-dimensional electron system at a copper surface5. Using low-temperature scanning tunnelling microscopy and spectroscopy, we embed the symmetries underlying the two-dimensional Dirac equation into electron lattices, and then visualize and shape the resulting ground states. These experiments show the existence within the system of linearly dispersing, massless quasi-particles accompanied by a density of states characteristic of graphene. We then tune the quantum tunnelling between lattice sites locally to adjust the phase accrual of propagating electrons. Spatial texturing of lattice distortions produces atomically sharp p–n and p–n–p junction devices with two-dimensional control of Dirac fermion density and the power to endow Dirac particles with mass6,7,8. Moreover, we apply scalar and vector potentials locally and globally to engender topologically distinct ground states and, ultimately, embedded gauge fields9,10,11,12, wherein Dirac electrons react to ‘pseudo’ electric and magnetic fields present in their reference frame but absent from the laboratory frame. We demonstrate that Landau levels created by these gauge fields can be taken to the relativistic magnetic quantum limit, which has so far been inaccessible in natural graphene. Molecular graphene provides a versatile means of synthesizing exotic topological electronic phases in condensed matter using tailored nanostructures.
590 citations
TL;DR: It is found that BN substrates result in extraordinarily flat graphene layers that display microscopic Moiré patterns arising from the relative orientation of the graphene and BN lattices.
Abstract: The use of boron nitride (BN) as a substrate for graphene nanodevices has attracted much interest since the recent report that BN greatly improves the mobility of charge carriers in graphene compared to standard SiO2 substrates. We have explored the local microscopic properties of graphene on a BN substrate using scanning tunneling microscopy. We find that BN substrates result in extraordinarily flat graphene layers that display microscopic Moire patterns arising from the relative orientation of the graphene and BN lattices. Gate-dependent dI/dV spectra of graphene on BN exhibit spectroscopic features that are sharper than those obtained for graphene on SiO2. We observe a significant reduction in local microscopic charge inhomogeneity for graphene on BN compared to graphene on SiO2.
586 citations
References
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TL;DR: Monocrystalline graphitic films are found to be a two-dimensional semimetal with a tiny overlap between valence and conductance bands and they exhibit a strong ambipolar electric field effect.
Abstract: We describe monocrystalline graphitic films, which are a few atoms thick but are nonetheless stable under ambient conditions, metallic, and of remarkably high quality. The films are found to be a two-dimensional semimetal with a tiny overlap between valence and conductance bands, and they exhibit a strong ambipolar electric field effect such that electrons and holes in concentrations up to 10 13 per square centimeter and with room-temperature mobilities of ∼10,000 square centimeters per volt-second can be induced by applying gate voltage.
55,532 citations
"The electronic properties of graphe..." refers background in this paper
...Be ause the DC magnetotransport properties ofgraphene are normally measured with the possibilityof tuning its ele troni density by a gate potential(Novoselov et al., 2004), it is important to ompute the ondu tivity kernel, sin e this has dire t experimentalrelevan e....
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...The same polarizability describes the screening of an external field perpendicular to the layers, like the one induced by a gate in electrically doped systems (Novoselov et al., 2004)....
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...Because the DC magnetotransport properties of graphene are normally measured with the possibility of tuning its electronic density by a gate potential (Novoselov et al., 2004), it is important to compute the conductivity kernel, since this has direct experimental relevance....
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...…studies of graphene sta ks have showed that, within reasing number of layers, the system be omes in reas-ingly metalli ( on entration of harge arriers at zero en-ergy gradually in reases), and there appear several typesof ele tron-and-hole-like arries (Morozov et al., 2005;Novoselov et al., 2004)....
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...The same polarizabilitydes ribes the s reening of an external eld perpendi ularto the layers, like the one indu ed by a gate in ele tri- ally doped systems (Novoselov et al., 2004)....
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TL;DR: Owing to its unusual electronic spectrum, graphene has led to the emergence of a new paradigm of 'relativistic' condensed-matter physics, where quantum relativistic phenomena can now be mimicked and tested in table-top experiments.
Abstract: Graphene is a rapidly rising star on the horizon of materials science and condensed-matter physics. This strictly two-dimensional material exhibits exceptionally high crystal and electronic quality, and, despite its short history, has already revealed a cornucopia of new physics and potential applications, which are briefly discussed here. Whereas one can be certain of the realness of applications only when commercial products appear, graphene no longer requires any further proof of its importance in terms of fundamental physics. Owing to its unusual electronic spectrum, graphene has led to the emergence of a new paradigm of 'relativistic' condensed-matter physics, where quantum relativistic phenomena, some of which are unobservable in high-energy physics, can now be mimicked and tested in table-top experiments. More generally, graphene represents a conceptually new class of materials that are only one atom thick, and, on this basis, offers new inroads into low-dimensional physics that has never ceased to surprise and continues to provide a fertile ground for applications.
35,293 citations
"The electronic properties of graphe..." refers background in this paper
...As the current status of the experiment and potential applications have recently been reviewed (Geim and Novoselov, 2007), in this article we mostly concentrate on the theory and more technical aspects of electronic properties of this exciting new material....
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...As the urrent status of the experimentand potential appli ations have re ently been reviewed(Geim and Novoselov, 2007), in this arti le we mostly on entrate on the theory and more te hni al aspe ts ofele troni properties of this ex iting new material....
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...It has also been suggested that Coulomb intera tionsare onsiderably enhan ed in smaller geometries, su has graphene quantum dots (Milton Pereira Junior et al.,2007), leading to unusual Coulomb blo kade e e ts 4(Geim and Novoselov, 2007) and perhaps to magneti phenomena su h as the Kondo e e t....
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...…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.,…...
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...Besides the unusual basic properties, graphene has the potential for a large number of applications (Geim and Novoselov, 2007), from chemical sensors (Chen et al....
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Book•
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01 Jan 1934
TL;DR: The theory of the slipline field is used in this article to solve the problem of stable and non-stressed problems in plane strains in a plane-strain scenario.
Abstract: Chapter 1: Stresses and Strains Chapter 2: Foundations of Plasticity Chapter 3: Elasto-Plastic Bending and Torsion Chapter 4: Plastic Analysis of Beams and Frames Chapter 5: Further Solutions of Elasto-Plastic Problems Chapter 6: Theory of the Slipline Field Chapter 7: Steady Problems in Plane Strain Chapter 8: Non-Steady Problems in Plane Strain
20,724 citations
TL;DR: This study reports an experimental study of a condensed-matter system (graphene, a single atomic layer of carbon) in which electron transport is essentially governed by Dirac's (relativistic) equation and reveals a variety of unusual phenomena that are characteristic of two-dimensional Dirac fermions.
Abstract: Quantum electrodynamics (resulting from the merger of quantum mechanics and relativity theory) has provided a clear understanding of phenomena ranging from particle physics to cosmology and from astrophysics to quantum chemistry. The ideas underlying quantum electrodynamics also influence the theory of condensed matter, but quantum relativistic effects are usually minute in the known experimental systems that can be described accurately by the non-relativistic Schrodinger equation. Here we report an experimental study of a condensed-matter system (graphene, a single atomic layer of carbon) in which electron transport is essentially governed by Dirac's (relativistic) equation. The charge carriers in graphene mimic relativistic particles with zero rest mass and have an effective 'speed of light' c* approximately 10(6) m s(-1). Our study reveals a variety of unusual phenomena that are characteristic of two-dimensional Dirac fermions. In particular we have observed the following: first, graphene's conductivity never falls below a minimum value corresponding to the quantum unit of conductance, even when concentrations of charge carriers tend to zero; second, the integer quantum Hall effect in graphene is anomalous in that it occurs at half-integer filling factors; and third, the cyclotron mass m(c) of massless carriers in graphene is described by E = m(c)c*2. This two-dimensional system is not only interesting in itself but also allows access to the subtle and rich physics of quantum electrodynamics in a bench-top experiment.
18,958 citations
"The electronic properties of graphe..." refers background or methods in this paper
...This amazing re-sult has been observed experimentally (Novoselov et al.,2005a; Zhang et al., 2005) as shown in Fig.20....
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...Adapted from(Novoselov et al., 2005a)....
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...Adapted from (Novoselov et al.,2005a).and hen e σxy,inc. = I/VH = ±4Ne2/h, whi h is thenaive expe tation....
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...The period of os illations ∆n = 4B/Φ0,where B is the applied eld and Φ0 is the ux quantum(Novoselov et al., 2005a).or equivalently: (Oσ+ + O†σ−)φ = (2E/ωc)φ , (100)where σ± = σx ± iσy, and we have de ned the dimen-sionless length s ale: ξ = y ℓB − ℓBk , (101)and 1D harmoni os illator operators: O =…...
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...…invery unusual ways when ompared to ordinary ele tronsif subje ted to magneti elds, leading to new physi alphenomena (Gusynin and Sharapov, 2005; Peres et al.,2006 ) su h as the anomalous integer quantum Hall ef-fe t (IQHE) measured experimentally (Novoselov et al.,2005a; Zhang et al., 2005)....
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