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•

Can Two-Dimensional Boron Superconduct?

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Evgeni S. Penev¹, Alex Kutana¹, Boris I. Yakobson¹•Institutions (1)

Rice University¹

25 Mar 2016-Nano Letters

TL;DR: First-principles analysis of electronic structure, phonon spectra, and electron-phonon coupling of selected 2D boron polymorphs show that the most stable structures predicted to feasibly form on a metal substrate should also exhibit intrinsic phonon-mediated superconductivity.

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Abstract: Two-dimensional boron is expected to exhibit various structural polymorphs, all being metallic. Additionally, its small atomic mass suggests strong electron–phonon coupling, which in turn can enable superconducting behavior. Here we perform first-principles analysis of electronic structure, phonon spectra, and electron–phonon coupling of selected 2D boron polymorphs and show that the most stable structures predicted to feasibly form on a metal substrate should also exhibit intrinsic phonon-mediated superconductivity, with estimated critical temperature in the range of Tc ≈ 10–20 K.

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358 citations

Journal Article•DOI•

Doping of Carbon Materials for Metal-Free Electrocatalysis.

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Chuangang Hu¹, Liming Dai¹•Institutions (1)

Case Western Reserve University¹

01 Feb 2019-Advanced Materials

TL;DR: An overview on the doping of carbon materials for metal-free electrocatalysis, especially the development of doping strategies and doping-induced structure and property changes for potential catalytic applications is presented.

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Abstract: Carbon atoms in the graphitic carbon skeleton can be replaced by heteroatoms with different electronegative from that of the carbon atom (i.e., heteroatom doping) to modulate the charge distribution over the carbon network. The charge modulation can be achieved via direct charge transfer with an electron acceptor/donor (i.e., charge transfer doping) or through introduction of defects (i.e., defective doping). Various doping strategies, including heteroatom doping, charge-transfer doping, and defective doping, have now been devised for modulating the charge distribution of numerous graphite carbon materials to impart new properties to carbon materials. Consequently, carbon nanomaterials with defined doping have recently become prominent members in the carbon family, promising for a variety of applications, including catalysis, energy conversion and storage, environmental remediation, and important chemical production and industrial processes. The purpose of this review is to present an overview on the doping of carbon materials for metal-free electrocatalysis, especially the development of doping strategies and doping-induced structure and property changes for potential catalytic applications. Current challenges and future perspectives in the doped carbon-based metal-free catalyst field are also discussed.

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358 citations

Journal Article•DOI•

Electronic and optical properties of strained graphene and other strained 2D materials: a review.

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Gerardo G. Naumis¹, Salvador Barraza-Lopez², M. Oliva-Leyva¹, Humberto Terrones³•Institutions (3)

National Autonomous University of Mexico¹, University of Arkansas², Rensselaer Polytechnic Institute³

21 Aug 2017-Reports on Progress in Physics

TL;DR: This review presents the state of the art in strain and ripple-induced effects on the electronic and optical properties of graphene by providing the crystallographic description of mechanical deformations, as well as the diffraction pattern for different kinds of representative deformation fields.

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Abstract: This review presents the state of the art in strain and ripple-induced effects on the electronic and optical properties of graphene. It starts by providing the crystallographic description of mechanical deformations, as well as the diffraction pattern for different kinds of representative deformation fields. Then, the focus turns to the unique elastic properties of graphene, and to how strain is produced. Thereafter, various theoretical approaches used to study the electronic properties of strained graphene are examined, discussing the advantages of each. These approaches provide a platform to describe exotic properties, such as a fractal spectrum related with quasicrystals, a mixed Dirac-Schrodinger behavior, emergent gravity, topological insulator states, in molecular graphene and other 2D discrete lattices. The physical consequences of strain on the optical properties are reviewed next, with a focus on the Raman spectrum. At the same time, recent advances to tune the optical conductivity of graphene by strain engineering are given, which open new paths in device applications. Finally, a brief review of strain effects in multilayered graphene and other promising 2D materials like silicene and materials based on other group-IV elements, phosphorene, dichalcogenide- and monochalcogenide-monolayers is presented, with a brief discussion of interplays among strain, thermal effects, and illumination in the latter material family.

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358 citations

Journal Article•DOI•

Pressure-controlled interlayer magnetism in atomically thin CrI3.

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Tingxin Li¹, Shengwei Jiang¹, Nikhil Sivadas¹, Zefang Wang¹, Yang Xu¹, Daniel Weber², Joshua E. Goldberger², Kenji Watanabe³, Takashi Taniguchi³, Craig J. Fennie¹, Kin Fai Mak¹, Jie Shan¹ - Show less +8 more•Institutions (3)

Cornell University¹, Ohio State University², National Institute for Materials Science³

28 Oct 2019-Nature Materials

TL;DR: In this paper, pressure-induced changes in the magnetic order of atomically thin van der Waals crystals are revealed and attributed to changes in stacking arrangement, and the interlayer ferromagnetic ground state is established in bulk CrI3 but not observed in native exfoliated thin films.

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Abstract: Stacking order can influence the physical properties of two-dimensional van der Waals materials1,2. Here we applied hydrostatic pressure up to 2 GPa to modify the stacking order in the van der Waals magnetic insulator CrI3. We observed an irreversible interlayer antiferromagnetic-to-ferromagnetic transition in atomically thin CrI3 by magnetic circular dichroism and electron tunnelling measurements. The effect was accompanied by a monoclinic-to-rhombohedral stacking-order change characterized by polarized Raman spectroscopy. Before the structural change, the interlayer antiferromagnetic coupling energy can be tuned up by nearly 100% with pressure. Our experiment reveals the interlayer ferromagnetic ground state, which is established in bulk CrI3 but not observed in native exfoliated thin films. The observed correlation between the magnetic ground state and the stacking order is in good agreement with first principles calculations3–8 and suggests a route towards nanoscale magnetic textures by moire engineering3,9. Pressure-induced changes in the magnetic order of atomically thin van der Waals crystals are revealed and attributed to changes in the stacking arrangement.

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357 citations

Journal Article•DOI•

Graphene-based semiconductor nanostructures

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Pavel B. Sorokin¹, Leonid A. Chernozatonskii¹•Institutions (1)

Russian Academy of Sciences¹

01 Feb 2013-Physics-Uspekhi

TL;DR: In this paper, the state-of-the-art in the field of semiconducting derivatives of GAs is summarized, including graphane, fluorographene, and diamane.

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Abstract: One of the current priorities in the physics and chemistry of graphene is the study of its semiconducting derivatives. This review summarizes the state of the art in this area of research. The structure and electronic properties of materials as such graphene ribbons, partially hydrogenated and fluorinated graphene, graphane, fluorographene, and diamane are discussed in detail.

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357 citations

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References

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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....
[...]
...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)....
[...]
...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)....
[...]
...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....
[...]
...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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