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•

Supported graphene from natural resources: easy preparation and applications.

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Eduardo Ruiz-Hitzky¹, Margarita Darder¹, Francisco M. Fernandes¹, Ezzouhra Zatile¹, Francisco Palomares¹, Pilar Aranda¹ - Show less +2 more•Institutions (1)

Spanish National Research Council¹

23 Nov 2011-Advanced Materials

TL;DR: The authors are grateful for funding from CICYT (Spain), project MAT2009-09960, MAT2010-18432 and project 2010MA0003 from CSIC-Academie Hassan II.

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Abstract: The authors are grateful for funding from CICYT (Spain), project MAT2009-09960, MAT2010-18432 and project 2010MA0003 from CSIC-Academie Hassan II. F. M. F. and E.Z. are indebted to the Spanish Ministry of Science & Innovation (MICINN) and the AECID (Spain), respectively, for their doctoral fellowships.

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154 citations

Journal Article•DOI•

Valley-protected backscattering suppression in silicon photonic graphene

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Xiao Dong Chen¹, Jian-Wen Dong•Institutions (1)

Sun Yat-sen University¹

10 Feb 2016-Physical Review B

TL;DR: In this paper, the authors studied the valley degree of freedom in all dielectric silicon photonic graphene and revisited the gap opening physics under inversion symmetry breaking by the viewpoint of nonzero valley Chern number.

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Abstract: In this paper, we study valley degree of freedom in all dielectric silicon photonic graphene. Photonic band gap opening physics under inversion symmetry breaking is revisited by the viewpoint of nonzero valley Chern number. Bulk valley modes with opposite orbital angular momentum are unveiled by inspecting time-varying electric fields. Topological transition is well illustrated through photonic Dirac Hamiltonian. Valley dependent edge states and the associated valley-protected backscattering suppression around Z-shape bend waveguide have been demonstrated.

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154 citations

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

...cones in low energy electronic band structure [1]....
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Journal Article•DOI•

A Guide to the Design of Electronic Properties of Graphene Nanoribbons

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Oleg V. Yazyev¹•Institutions (1)

École Polytechnique Fédérale de Lausanne¹

04 Mar 2013-arXiv: Mesoscale and Nanoscale Physics

TL;DR: A pedagogical overview of the various degrees of freedom in the atomic structure and interactions that researchers can use to tailor the electronic structure of graphene nanostructures through synthetic techniques.

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Abstract: Graphene nanoribbons (GNRs) are one-dimensional nanostructures predicted to display a rich variety of electronic behaviors. Depending on their structure, GNRs realize metallic and semiconducting electronic structures with band gaps that can be tuned across broad ranges. Certain GNRs also exhibit a peculiar gapped magnetic phase for which the half-metallic state can be induced as well as the topologically non-trivial quantum spin Hall electronic phase. Because their electronic properties are highly tunable, GNRs have quickly become a popular subject of research toward the design of graphene-based nanostructures for technological applications. This Account presents a pedagogical overview of the various degrees of freedom in the atomic structure and interactions that researchers can use to tailor the electronic structure of these materials. The Account provides a broad picture of relevant physical concepts that would facilitate the rational design of GNRs with desired electronic properties through synthetic techniques.

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154 citations

Journal Article•DOI•

Electronic structures and unusually robust bandgap in an ultrahigh-mobility layered oxide semiconductor, Bi2O2Se

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Cheng Chen¹, Meixiao Wang², Jinxiong Wu³, Huixia Fu⁴, Haifeng Yang², Zhen Tian², Teng Tu³, Han Peng¹, Yan Sun⁵, Xiang Xu⁶, Xiang Xu⁷, Juan Jiang², Juan Jiang⁸, Juan Jiang⁷, Niels B. M. Schröter¹, Niels B. M. Schröter⁹, Yiwei Li¹, Ding Pei¹, Shuai Liu², Sandy Adhitia Ekahana¹, Hongtao Yuan¹⁰, Jiamin Xue², Gang Li², Jin-Feng Jia¹¹, Zhongkai Liu², Binghai Yan⁴, Hailin Peng³, Yulin Chen², Yulin Chen¹, Yulin Chen⁶ - Show less +26 more•Institutions (11)

University of Oxford¹, Chinese Academy of Sciences², Peking University³, Weizmann Institute of Science⁴, Max Planck Society⁵, Tsinghua University⁶, Lawrence Berkeley National Laboratory⁷, Pohang University of Science and Technology⁸, Paul Scherrer Institute⁹, Nanjing University¹⁰, Shanghai Jiao Tong University¹¹

01 Sep 2018-Science Advances

TL;DR: The unusual spatial uniformity of the bandgap without undesired in-gap states on the sample surface with up to ~50% defects makes Bi2O2Se an ideal semiconductor for future electronic applications.

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Abstract: Semiconductors are essential materials that affect our everyday life in the modern world Two-dimensional semiconductors with high mobility and moderate bandgap are particularly attractive today because of their potential application in fast, low-power, and ultrasmall/thin electronic devices We investigate the electronic structures of a new layered air-stable oxide semiconductor, Bi2O2Se, with ultrahigh mobility (~28 × 105 cm2/V⋅s at 20 K) and moderate bandgap (~08 eV) Combining angle-resolved photoemission spectroscopy and scanning tunneling microscopy, we mapped out the complete band structures of Bi2O2Se with key parameters (for example, effective mass, Fermi velocity, and bandgap) The unusual spatial uniformity of the bandgap without undesired in-gap states on the sample surface with up to ~50% defects makes Bi2O2Se an ideal semiconductor for future electronic applications In addition, the structural compatibility between Bi2O2Se and interesting perovskite oxides (for example, cuprate high–transition temperature superconductors and commonly used substrate material SrTiO3) further makes heterostructures between Bi2O2Se and these oxides possible platforms for realizing novel physical phenomena, such as topological superconductivity, Josephson junction field-effect transistor, new superconducting optoelectronics, and novel lasers

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154 citations

Journal Article•DOI•

Facile, Noncovalent Decoration of Graphene Oxide Sheets with Nanocrystals

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Ganhua Lu¹, Shun Mao¹, Sungjin Park², Rodney S. Ruoff², Junhong Chen¹ - Show less +1 more•Institutions (2)

University of Wisconsin–Milwaukee¹, University of Texas at Austin²

08 Mar 2009-Nano Research

TL;DR: In this article, the authors used an electrostatic force-directed assembly technique at room temperature for dry decoration of graphene oxide sheets with aerosol Ag nanocrystals synthesized from an arc plasma source.

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Abstract: Facile dry decoration of graphene oxide sheets with aerosol Ag nanocrystals synthesized from an arc plasma source has been demonstrated using an electrostatic force directed assembly technique at room temperature. The Ag nanocrystal-graphene oxide hybrid structure was characterized by transmission electron microscopy (TEM) and selected area diffraction. The ripening of Ag nanocrystals on a graphene oxide sheet was studied by consecutive TEM imaging of the same region on a sample after heating in Ar at elevated temperatures of 100 °C, 200 °C, and 300 °C. The average size of Ag nanocrystals increased and the number density decreased after the annealing process. In particular, migration and coalescence of Ag nanocrystals were observed at a temperature as low as 100 °C, suggesting a van der Waals interaction between the Ag nanocrystal and the graphene oxide sheet. The availability of affordable graphene-nanocrystal structures and their fundamental properties will open up new opportunities for nanoscience and nanotechnology and accelerate their applications.

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153 citations

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

...Hybrid materials consisting of nanocrystals distributed on the surface of graphene could potentially display not only the unique properties of nanocrystals [21, 22] and those of graphene [1, 3, 23, 24], but also additional novel properties due to the interaction between the nanocrystals and the graphene....
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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....
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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 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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