The electronic properties of graphene

doi:10.1103/REVMODPHYS.81.109

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The electronic properties of graphene

Journal Article•DOI•

The electronic properties of graphene

A. H. Castro Neto¹, Francisco Guinea², Nuno M. R. Peres³, Kostya S. Novoselov⁴, Andre K. Geim⁴ - Show less +1 more•Institutions (4)

Boston University¹, Spanish National Research Council², University of Minho³, University of Manchester⁴

14 Jan 2009-Reviews of Modern Physics (American Physical Society)-Vol. 81, Iss: 1, pp 109-162

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.

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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 Article•DOI•

Zinc oxide nanostructures: from growth to application

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Jorge Gomez¹, Onur Tigli¹•Institutions (1)

University of Miami¹

01 Jan 2013-Journal of Materials Science

TL;DR: A comprehensive review on the growth methods currently employed in research, industry, and academia to understand what protocols are available to meet specific needs in nanotechnology is presented in this paper, where the current state-of-the-art applications employing ZnO nanostructures at their core.

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Abstract: Zinc oxide’s (ZnO) physical and chemical properties make it a viable and extremely attractive compound to use in a variety of nanotechnology applications. Some of these applications include biomedical, energy, sensors, and optics. As the research in ZnO nanostructures continue to grow, it has inspired a whole host of new innovative applications. Complementing its unique chemical qualities, it also has a simple crystal-growth technology and offers significantly lower fabrication costs when compared to other semiconductors used in nanotechnology. Several processes have been developed in order to synthesize high quality ZnO nanostructures—specifically in the case of nanowires. Here we offer a comprehensive review on the growth methods currently employed in research, industry, and academia to understand what protocols are available to meet specific needs in nanotechnology. Methods examined include: the vapor–liquid–solid, physical vapor deposition, chemical vapor deposition, metal–organic chemical vapor deposition, and the hydrothermal-based chemical approach. Each of these methods is discussed and their strengths and weaknesses are analyzed with objective comparison metrics. In addition, we study the current state-of-the-art applications employing ZnO nanostructures at their core. A historical perspective on the evolution of the field and the accompanying literature are also presented.

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191 citations

Journal Article•DOI•

Strain and curvature induced evolution of electronic band structures in twisted graphene bilayer.

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Wei Yan¹, Wen-Yu He¹, Zhaodong Chu¹, Mengxi Liu², Lan Meng¹, Rui-Fen Dou¹, Yanfeng Zhang², Zhongfan Liu², Jia-Cai Nie¹, Lin He¹ - Show less +6 more•Institutions (2)

Beijing Normal University¹, Peking University²

12 Jul 2013-Nature Communications

TL;DR: The results suggest that strained graphene bilayer could be an ideal platform to realize the high-temperature zero-field quantum valley Hall effect.

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Abstract: It is well established that strain and geometry could affect the band structure of graphene monolayer dramatically. Here we study the evolution of local electronic properties of a twisted graphene bilayer induced by a strain and a high curvature, which are found to strongly affect the local band structures of the twisted graphene bilayer. The energy difference of the two low-energy van Hove singularities decreases with increasing lattice deformation and the states condensed into well-defined pseudo-Landau levels, which mimic the quantization of massive chiral fermions in a magnetic field of about 100 T, along a graphene wrinkle. The joint effect of strain and out-of-plane distortion in the graphene wrinkle also results in a valley polarization with a significant gap. These results suggest that strained graphene bilayer could be an ideal platform to realize the high-temperature zero-field quantum valley Hall effect.

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190 citations

Journal Article•DOI•

Strained graphene: tight-binding and density functional calculations

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Ricardo M. Ribeiro¹, Vitor M. Pereira², Nuno M. R. Peres¹, Patrick R. Briddon³, A. H. Castro Neto² - Show less +1 more•Institutions (3)

University of Minho¹, Boston University², Newcastle University³

01 Nov 2009-New Journal of Physics

TL;DR: In this article, the authors determine the band structure of graphene under strain using density functional calculations and extract the best fit to the tight-binding hopping parameters used in a recent microscopic model of strained graphene.

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Abstract: We determine the band structure of graphene under strain using density functional calculations. The ab initio band structure is then used to extract the best fit to the tight-binding hopping parameters used in a recent microscopic model of strained graphene. It is found that the hopping parameters may increase or decrease upon increasing strain, depending on the orientation of the applied stress. The fitted values are compared with an available parameterization for the dependence of the orbital overlap on the distance separating the two carbon atoms. It is also found that strain does not induce a gap in graphene, at least for deformations up to 10%.

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190 citations

Journal Article•DOI•

Enhanced thermopower of graphene films with oxygen plasma treatment.

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Ni Xiao¹, Xiaochen Dong², Li Song³, Da-Yong Liu¹, Da-Yong Liu⁴, Yee Yan Tay¹, Shixin Wu¹, Lain-Jong Li¹, Yang Zhao¹, Ting Yu¹, Hua Zhang¹, Wei Huang², Huey Hoon Hng¹, Pulickel M. Ajayan³, Qingyu Yan¹ - Show less +11 more•Institutions (4)

Nanyang Technological University¹, Nanjing University of Posts and Telecommunications², Rice University³, Chinese Academy of Sciences⁴

23 Mar 2011-ACS Nano

TL;DR: It is shown that the maximum thermopower of few layers graphene (FLG) films could be greatly enhanced up to ∼700 μV/K after oxygen plasma treatment, due to generation of local disordered carbon that opens the band gap.

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Abstract: Inthiswork,weshowthatthemaximumthermopoweroffewlayersgraphene(FLG) films could be greatly enhanced up to ∼700 μV/K after oxygen plasma treatment. The electrical conductivities of these plasma treated FLG films remain high, for example, ∼10 4 S/m, which results in power factors as high as ∼4.5 � 10 � 3 WK � 2 m � 1 . In comparison, the pristine FLG films show a maximum thermopower of ∼80 μV/K with an electrical conductivity of ∼5 � 10 4 S/m. The proposed mechanism is due to generation of local disordered carbon that opens the band gap. Measured thermopowers of single-layer graphene (SLG) films and reduced graphene oxide (rGO) films were in the range of � 40 to 50 and � 10 to 20 μV/K, respectively. However, such oxygen plasma treatment is not suitable for SLG and rGO films. The SLG films were easily destroyed during the treatment while the electrical conductivity of rGO films is too low.

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190 citations

Journal Article•DOI•

Measurement of the thermal conductance of the graphene/SiO2 interface

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Kin Fai Mak, Chun Hung Lui¹, Tony F. Heinz¹•Institutions (1)

Columbia University¹

30 Nov 2010-Applied Physics Letters

TL;DR: In this article, the authors examined the interfacial thermal conductance of single and multilayer graphene samples prepared on fused SiO2 substrates by mechanical exfoliation of graphite.

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Abstract: We have examined the interfacial thermal conductance GK of single and multilayer graphene samples prepared on fused SiO2 substrates by mechanical exfoliation of graphite. By using an ultrafast optical pump pulse and monitoring the transient reflectivity on the picosecond time scale, we obtained an average value of GK of GK=5000 W/cm2 K for the graphene/SiO2 interface at room temperature. We observed significant variation in GK between individual samples, but found no systematic dependence on the thickness of the graphene layers.

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190 citations

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Journal Article•DOI•

Electric Field Effect in Atomically Thin Carbon Films

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Kostya S. Novoselov¹, Andre K. Geim¹, Sergey V. Morozov, Da Jiang¹, Y. Zhang¹, S. V. Dubonos, Irina V. Grigorieva¹, A. A. Firsov - Show less +4 more•Institutions (1)

University of Manchester¹

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.

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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.

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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....
[...]
...…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)....
[...]

Journal Article•DOI•

The rise of graphene

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Andre K. Geim¹, Kostya S. Novoselov¹•Institutions (1)

University of Manchester¹

01 Mar 2007-Nature Materials

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.

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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.

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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....
[...]
...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•

Theory of elasticity

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Stephen P. Timoshenko, James Norman Goodier

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.

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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

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20,724 citations

Journal Article•DOI•

Two-dimensional gas of massless Dirac fermions in graphene

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Kostya S. Novoselov¹, A. K. Geim¹, Sergey V. Morozov, Da Jiang¹, Mikhail I. Katsnelson², Irina V. Grigorieva¹, S. V. Dubonos, A. A. Firsov - Show less +4 more•Institutions (2)

University of Manchester¹, Radboud University Nijmegen²

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.

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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.

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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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