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•

Porous Graphene as the Ultimate Membrane for Gas Separation

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De-en Jiang¹, Valentino R. Cooper¹, Sheng Dai¹•Institutions (1)

Oak Ridge National Laboratory¹

23 Sep 2009-Nano Letters

TL;DR: Porous graphene sheets are proposed as one-atom-thin, highly efficient, and highly selective membranes for gas separation, which could have widespread impact on numerous energy and technological applications; including carbon sequestration, fuel cells, and gas sensors.

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Abstract: We investigate the permeability and selectivity of graphene sheets with designed subnanometer pores using first principles density functional theory calculations. We find high selectivity on the order of 10(8) for H(2)/CH(4) with a high H(2) permeance for a nitrogen-functionalized pore. We find extremely high selectivity on the order of 10(23) for H(2)/CH(4) for an all-hydrogen passivated pore whose small width (at 2.5 A) presents a formidable barrier (1.6 eV) for CH(4) but easily surmountable for H(2) (0.22 eV). These results suggest that these pores are far superior to traditional polymer and silica membranes, where bulk solubility and diffusivity dominate the transport of gas molecules through the material. Recent experimental investigations, using either electron beams or bottom-up synthesis to create pores in graphene, suggest that it may be possible to employ such techniques to engineer variable-sized, graphene nanopores to tune selectivity and molecular diffusivity. Hence, we propose using porous graphene sheets as one-atom-thin, highly efficient, and highly selective membranes for gas separation. Such a pore could have widespread impact on numerous energy and technological applications; including carbon sequestration, fuel cells, and gas sensors.

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894 citations

Journal Article•DOI•

Optical separation of mechanical strain from charge doping in graphene

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Ji Eun Lee¹, Ji Eun Lee², Gwanghyun Ahn¹, Jihye Shim¹, Young Sik Lee¹, Sunmin Ryu¹ - Show less +2 more•Institutions (2)

Kyung Hee University¹, Korea Research Institute of Standards and Science²

28 Aug 2012-Nature Communications

TL;DR: It is suggested that substrate-mediated mechanical strain is a ubiquitous phenomenon in two-dimensional materials and the proposed analysis will be of great use in characterizing graphene-based materials and devices.

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Abstract: Because of its superior stretchability, graphene exhibits rich structural deformation behaviours and its strain engineering has proven useful in modifying its electronic and magnetic properties. Despite the strain-sensitivity of the Raman G and 2D modes, the optical characterization of the native strain in graphene on silica substrates has been hampered by excess charges interfering with both modes. Here we show that the effects of strain and charges can be optically separated from each other by correlation analysis of the two modes, enabling simple quantification of both. Graphene with in-plane strain randomly occurring between −0.2% and 0.4% undergoes modest compression (−0.3%) and significant hole doping on thermal treatments. This study suggests that substrate-mediated mechanical strain is a ubiquitous phenomenon in two-dimensional materials. The proposed analysis will be of great use in characterizing graphene-based materials and devices. The spectral position of Raman peaks is a useful diagnostic for determining the degree of strain and excess electronic charges present in graphene. This study demonstrates that these two contributions can be separated from each other and therefore be obtained at the same time.

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882 citations

Journal Article•DOI•

Luminscent Graphene Quantum Dots for Organic Photovoltaic Devices

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Vinay Gupta¹, Neeraj Chaudhary¹, Ritu Srivastava¹, G. D. Sharma¹, Ramil Bhardwaj¹, Suresh Chand¹ - Show less +2 more•Institutions (1)

National Physical Laboratory¹

14 Jun 2011-Journal of the American Chemical Society

TL;DR: It is demonstrated that graphene quantum dots blended with regioregular poly(3-hexylthiophene-2,5-diyl) or poly(2-methoxy-5-(2-ethylhexyloxy)-1,4phenylenevinylene) polymer results in a significant improvement in the OPV characteristics as compared to GSs blended conjugated polymers.

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Abstract: Recent research in organic photovoltaic (OPV) is largely focused on developing low cost OPV materials such as graphene. However, graphene sheets (GSs) blended conjugated polymers are known to show inferior OPV characteristics as compared to fullerene adduct blended with conjugated polymer. Here, we demonstrate that graphene quantum dots blended with regioregular poly(3-hexylthiophene-2,5-diyl) or poly(2-methoxy-5-(2-ethylhexyloxy)-1,4phenylenevinylene) polymer results in a significant improvement in the OPV characteristics as compared to GSs blended conjugated polymers. This work has implications for inexpensive and efficient solar cells as well as organic light emitting diodes.

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881 citations

Journal Article•DOI•

Pyridinic N doped graphene: synthesis, electronic structure, and electrocatalytic property

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Zhiqiang Luo¹, San Hua Lim, Zhiqun Tian, Jingzhi Shang¹, Linfei Lai¹, Brian MacDonald, Chao Fu, Zexiang Shen¹, Ting Yu², Ting Yu¹, Jianyi Lin - Show less +7 more•Institutions (2)

Nanyang Technological University¹, National University of Singapore²

24 May 2011-Journal of Materials Chemistry

TL;DR: In this article, a single layer graphene was synthesized with pure pyridinic N by thermal chemical vapour deposition of hydrogen and ethylene on Cu foils in the presence of ammonia.

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Abstract: Different C–N bonding configurations in nitrogen (N) doped carbon materials have different electronic structures. Carbon materials doped with only one kind of C–N bonding configuration are an excellent platform for studying doping effects on the electronic structure and physical/chemical properties. Here we report synthesis of single layer graphene doped with pure pyridinic N by thermal chemical vapour deposition of hydrogen and ethylene on Cu foils in the presence of ammonia. By adjusting the flow rate of ammonia, the atomic ratio of N and C can be modulated from 0 to 16%. The domain like distribution of N incorporated in graphene was revealed by the imaging of Raman spectroscopy and time-of-flight secondary ion mass spectrometry. The ultraviolet photoemission spectroscopy investigation demonstrated that the pyridinic N efficiently changed the valence band structure of graphene, including the raising of density of π states near the Fermi level and the reduction of work function. Such pyridinic N doping in carbon materials was generally considered to be responsible for their oxygen reduction reaction (ORR) activity. The 2e reduction mechanism of ORR on our CNxgraphene revealed by rotating disk electrode voltammetry indicated that the pyridinic N may not be an effective promoter for ORR activity of carbon materials as previously expected.

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875 citations

Journal Article•DOI•

STM Spectroscopy of ultra-flat graphene on hexagonal boron nitride

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Jiamin Xue, Javier Sanchez-Yamagishi, Daniel Bulmash, Philippe Jacquod, Kenji Watanabe, T. Taniguchi, Pablo Jarillo-Herrero, Brian J. LeRoy¹ - Show less +4 more•Institutions (1)

University of Arizona¹

13 Feb 2011-arXiv: Materials Science

TL;DR: In this article, the authors used scanning tunneling microscopy to show that placing graphene on hexagonal boron nitride (hBN) yields improved device performance and showed that placing the graphene on hBN improved the device performance.

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Abstract: Graphene has demonstrated great promise for future electronics technology as well as fundamental physics applications because of its linear energy-momentum dispersion relations which cross at the Dirac point[1, 2]. However, accessing the physics of the low density region at the Dirac point has been difficult because of the presence of disorder which leaves the graphene with local microscopic electron and hole puddles[3–5], resulting in a finite density of carriers even at the charge neutrality point. Efforts have been made to reduce the disorder by suspending graphene, leading to fabrication challenges and delicate devices which make local spectroscopic measurements difficult[6, 7]. Recently, it has been shown that placing graphene on hexagonal boron nitride (hBN) yields improved device performance[8]. In this letter, we use scanning tunneling microscopy to show that

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873 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)....
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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....
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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•

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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