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Journal ArticleDOI

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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Citations
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Journal ArticleDOI
TL;DR: Electronic transport measurements on thin Bi2Se3 devices are reported and it is shown that the density of the surface states can be modulated via the electric field effect by using a top-gate with a high-k dielectric insulator.
Abstract: Electronic transport experiments involving the topologically protected states found at the surface of Bi2Se3 and other topological insulators require fine control over carrier density, which is challenging with existing bulk-doped material. Here we report on electronic transport measurements on thin (<100 nm) Bi2Se3 devices and show that the density of the surface states can be modulated via the electric field effect by using a top-gate with a high-k dielectric insulator. The conductance dependence on geometry, gate voltage, and temperature all indicate that transport is governed by parallel surface and bulk contributions. Moreover, the conductance dependence on top-gate voltage is ambipolar, consistent with tuning between electrons and hole carriers at the surface.

258 citations

Journal ArticleDOI
TL;DR: Oxidized GNRs (ox-GNRs) outperform all of the other materials studied here in terms of energy density and present a first charge capacity of approximately 1400 mA h g(-1) with a low Coulombic efficiency for the first cycle.
Abstract: Herein, we report the electrochemical Li intake capacity of carbonaceous one-dimensional graphene nanoribbons (GNRs) obtained by unzipping pristine multiwalled carbon nanotubes (MWCNTs). We have found that nanotubes with diameters of ∼50 nm present a smaller reversible capacity than conventional mesocarbon microbead (MCMB) powder. Reduced GNRs improve the capacity only marginally over the MCMB reference but present a lower Coulombic efficiency as well as a higher capacity loss per cycle. Oxidized GNRs (ox-GNRs) outperform all of the other materials studied here in terms of energy density. They present a first charge capacity of ∼1400 mA h g−1 with a low Coulombic efficiency for the first cycle (∼53%). The reversible capacity of ox-GNRs is in the range of 800 mA h g−1, with a capacity loss per cycle of ∼3% for early cycles and a decreasing loss rate for subsequent cycles.

258 citations

Journal ArticleDOI
TL;DR: Spectroscopic studies of electronic phenomena in graphene are reviewed in this article, where a variety of methods and techniques are surveyed, from quasiparticle spectroscopies (tunneling, photoemission) to methods probing density and current response (infrared optics, Raman) to scanning probe nanoscopy and ultrafast pump-probe experiments.
Abstract: Spectroscopic studies of electronic phenomena in graphene are reviewed. A variety of methods and techniques are surveyed, from quasiparticle spectroscopies (tunneling, photoemission) to methods probing density and current response (infrared optics, Raman) to scanning probe nanoscopy and ultrafast pump-probe experiments. Vast complimentary information derived from these investigations is shown to highlight unusual properties of Dirac quasiparticles and many-body interaction effects in the physics of graphene. © 2014 American Physical Society.

258 citations


Cites background from "The electronic properties of graphe..."

  • ...Next, shifting the Dirac point in the k-space away from the K (K′) points (Dietl et al., 2008; Farjam and Rafii-Tabar, 2009; Ni et al., 2008a, 2009a; Pereira and Castro Neto, 2009). is analogous to the effect induced by an external magnetic field applied perpendicular to the graphene plane....

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  • ...Unless Dt and Db are precisely equal or precisely opposite, the modification of the band gap ∆ and the shift of the Fermi energy EF occur simultaneously (Castro et al., 2007; McCann, 2006; McCann and Fal’ko, 2006)....

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  • ...In this section we summarize basic facts about the SLG band-structure within the independent electron approximation (Castro Neto et al., 2009)....

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  • ...The concept of 2D Dirac quasiparticles offers a 17See Castro et al. (2007); Oostinga et al. (2008); Szafranek et al. (2010); and Xia et al. (2010). unifying description of the gross features revealed in all spectroscopic and transport probes....

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  • ...D) 1See Castro Neto et al. (2009); Das Sarma et al. (2011); Katsnelson (2012); Kotov et al. (2012); McCann and Koshino (2013); and Peres (2010)....

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Journal ArticleDOI
TL;DR: It is shown that graphene deposited on a substrate has a non-negligible density of atomic scale defects and the effect of such impurities on electron transport is evaluated by mimicking them with hydrogen adsorbates and measuring the induced changes in both mobility and Raman intensity.
Abstract: We show that graphene deposited on a substrate has a non-negligible density of atomic scale defects. This is evidenced by a previously unnoticed D peak in the Raman spectra with intensity of ∼1% with respect to the G peak. We evaluated the effect of such impurities on electron transport by mimicking them with hydrogen adsorbates and measuring the induced changes in both mobility and Raman intensity. If the intervalley scatterers responsible for the D peak are monovalent, their concentration is sufficient to account for the limited mobilities currently achievable in graphene on a substrate.

257 citations

Journal ArticleDOI
TL;DR: A study of intravalley and intervalley double-resonance Raman processes mediated by static potentials in rotationally stacked bilayer graphene is presented and the peak properties depend on the mismatch rotation angle and can be used as an optical signature for superlattices in bilayers graphene.
Abstract: When two identical two-dimensional periodic structures are superposed, a mismatch rotation angle between the structures generates a superlattice. This effect is commonly observed in graphite, where the rotation between graphene layers generates Moire patterns in scanning tunneling microscopy images. Here, a study of intravalley and intervalley double-resonance Raman processes mediated by static potentials in rotationally stacked bilayer graphene is presented. The peak properties depend on the mismatch rotation angle and can be used as an optical signature for superlattices in bilayer graphene. An atomic force microscopy system is used to produce and identify specific rotationally stacked bilayer graphenes that demonstrate the validity of our model.

257 citations

References
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Journal ArticleDOI
22 Oct 2004-Science
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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Journal ArticleDOI
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
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

Journal ArticleDOI
10 Nov 2005-Nature
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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Book
01 Jan 1939

14,299 citations