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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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Journal ArticleDOI
TL;DR: In this paper, the authors reviewed the use of Raman spectroscopy in the characterization of sp2 hybridized carbon samples containing defects and discussed the possible influence of both phonon confinement and curvature of aromatic planes on the shape of the Raman spectrum.
Abstract: sp2 hybridized carbons constitute a broad class of solid phases composed primarily of elemental carbon and can be either synthetic or naturally occurring Some examples are graphite, chars, soot, graphene, carbon nanotubes, pyrolytic carbon, and diamond-like carbon They vary from highly ordered to completely disordered solids and detailed knowledge of their internal structure and composition is of utmost importance for the scientific and engineering communities working with these materials Multiwavelength Raman spectroscopy has proven to be a very powerful and non-destructive tool for the characterization of carbons containing both aromatic domains and defects and has been widely used since the 1980s Depending on the material studied, some specific spectroscopic parameters (eg, band position, full width at half maximum, relative intensity ratio between two bands) are used to characterize defects This paper is addressed first to (but not limited to) the newcomer in the field, who needs to be guided due to the vast literature on the subject, in order to understand the physics at play when dealing with Raman spectroscopy of graphene-based solids We also give historical aspects on the development of the Raman spectroscopy technique and on its application to sp2 hybridized carbons, which are generally not presented in the literature We review the way Raman spectroscopy is used for sp2 based carbon samples containing defects As graphene is the building block for all these materials, we try to bridge these two worlds by also reviewing the use of Raman spectroscopy in the characterization of graphene and nanographenes (eg, nanotubes, nanoribbons, nanocones, bombarded graphene) Counterintuitively, because of the Dirac cones in the electronic structure of graphene, Raman spectra are driven by electronic properties: Phonons and electrons being coupled by the double resonance mechanism This justifies the use of multiwavelength Raman spectroscopy to better characterize these materials We conclude with the possible influence of both phonon confinement and curvature of aromatic planes on the shape of Raman spectra, and discuss samples to be studied in the future with some complementary technique (eg, high resolution transmission electron microscopy) in order to disentangle the influence of structure and defects

244 citations

Journal ArticleDOI
TL;DR: Results demonstrate plasma-based functionalization of graphene surfaces is a viable approach to manipulate the thermal boundary conductance.
Abstract: Graphene-based devices have garnered tremendous attention due to the unique physical properties arising from this purely two-dimensional carbon sheet leading to tremendous efficiency in the transport of thermal carriers (i.e., phonons). However, it is necessary for this two-dimensional material to be able to efficiently transport heat into the surrounding 3D device architecture in order to fully capitalize on its intrinsic transport capabilities. Therefore, the thermal boundary conductance at graphene interfaces is a critical parameter in the realization of graphene electronics and thermal solutions. In this work, we examine the role of chemical functionalization on the thermal boundary conductance across metal/graphene interfaces. Specifically, we metalize graphene that has been plasma functionalized and then measure the thermal boundary conductance at Al/graphene/SiO2 contacts with time domain thermoreflectance. The addition of adsorbates to the graphene surfaces are shown to influence the cross plane t...

244 citations

Journal ArticleDOI
TL;DR: It is argued that the creation of stringent standards for graphene characterization and production, taking into account both the physical properties, as well as the requirements from the particular application, is the only way forward to create a healthy and reliable worldwide graphene market.
Abstract: There are hundreds of companies worldwide claiming to produce "graphene," showing a large variation in its properties. A systematic and reliable protocol is developed to test graphene quality using electron microscopy, atomic force microscopy, Raman spectroscopy, elemental analysis, X-ray photoelectron spectrometry, and scanning and transmission electron microscopy, which is used to study graphene from 60 producers. The statistical nature of the liquid-phase exfoliation of graphite is established. It is shown that the current classification of graphene flakes used in the market is erroneous. A new classification is proposed in terms of distribution functions for number of layers and flake size. It is shown unequivocally that the quality of the graphene produced in the world today is rather poor, not optimal for most applications, and most companies are producing graphite microplatelets. This is possibly the main reason for the slow development of graphene applications, which usually require a customized solution in terms of graphene properties. It is argued that the creation of stringent standards for graphene characterization and production, taking into account both the physical properties, as well as the requirements from the particular application, is the only way forward to create a healthy and reliable worldwide graphene market.

243 citations

Journal ArticleDOI
TL;DR: It is demonstrated that the wrinkles observed in the scanning tunneling microscopy study have lower electrical conductance and are characterized by the presence of midgap states, which is in agreement with recent theoretical predictions.
Abstract: We report on the scanning tunneling microscopy study of a new class of corrugations in exfoliated monolayer graphene sheets, that is, wrinkles ∼10 nm in width and ∼3 nm in height. We found such corrugations to be ubiquitous in graphene and have distinctly different properties when compared to other regions of graphene. In particular, a “three-for-six” triangular pattern of atoms is exclusively and consistently observed on wrinkles, suggesting the local curvature of the wrinkle provides a sufficient perturbation to break the 6-fold symmetry of the graphene lattice. Through scanning tunneling spectroscopy, we further demonstrate that the wrinkles have lower electrical conductance and are characterized by the presence of midgap states, which is in agreement with recent theoretical predictions. The observed wrinkles are likely important for understanding the electrical properties of graphene.

243 citations

Journal ArticleDOI
TL;DR: In this paper, the authors give an overview of the developing field of spintronics and outline the experimental and theoretical state-of-the-art of the art. But their focus is on van der Waals heterostructures, which consist of stacks of two-dimensional materials in precisely controlled order.
Abstract: Controlled spin transport in graphene and other two-dimensional materials has become increasingly promising for applications in devices. Of particular interest are custom-tailored heterostructures, known as van der Waals heterostructures, that consist of stacks of two-dimensional materials in a precisely controlled order. This Colloquium gives an overview of this developing field of spintronics and outlines the experimental and theoretical state of the art.

243 citations


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

  • ...Graphene consists of a single layer of sp2 hybridized carbon atoms (Castro Neto et al., 2009; Katsnelson, 2007)....

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  • ...…20 References 20 I. INTRODUCTION Since the discovery of graphene, the field of twodimensional (2D) materials have become one of the hot topics in solid state physics, mainly because of their prominent mechanical, optical, electrical and magnetic properties (Castro Neto et al., 2009)....

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  • ...…are relevant reviews on spin transport (Chappert et al., 2007; Meservey and Tedrow, 1994; Wolf et al., 2006; Žutić et al., 2004), graphene (Castro Neto et al., 2009; Das Sarma et al., 2011; Peres, 2010), and graphene spintronics (Garcia et al., 2018; Gurram et al., 2018; Han et al., 2012;…...

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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