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•

Microscopic theory of absorption and ultrafast many-particle kinetics in graphene

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Ermin Malic¹, Torben Winzer¹, Evgeny Bobkin¹, Andreas Knorr¹•Institutions (1)

Technical University of Berlin¹

10 Nov 2011-Physical Review B

TL;DR: In this article, the relaxation kinetics of optically excited charge carriers in graphene focusing on the time-, momentum-, and angle-resolved interplay between carrier-carrier and carrier-phonon scattering channels were investigated.

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Abstract: We investigate the relaxation kinetics of optically excited charge carriers in graphene focusing on the time-, momentum-, and angle-resolved interplay between carrier-carrier and carrier-phonon scattering channels. To benchmark the theoretical approach, we first discuss the linear absorption spectrum of graphene. In agreement with recent experimental results, our calculations reveal: (i) a pronounced excitonic effect at the saddle point, (ii) a constant absorbance in the visible region, and (iii) a drop-off for energies close to the Dirac point. After a nonlinear optical excitation, we observe that $\ensuremath{\Gamma}$-LO phonons efficiently and quickly redistribute the initially highly anisotropic nonequilibrium carrier distribution. In contrast, Coulomb-induced carrier relaxation is preferably carried out directly toward the Dirac point leading to an ultrafast thermalization of the carrier system. We evaluate the temporal dynamics of optical and acoustic phonons and discuss the energy dissipation arising from phonon-induced intra- and interband scattering. Furthermore, we investigate the influence of diagonal and off-diagonal many-particle dephasing on the ultrafast carrier relaxation dynamics. The gained insights contribute to a better microscopic understanding of optical and electronic properties of graphene.

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272 citations

Journal Article•DOI•

Electronic structure of few-layer graphene: experimental demonstration of strong dependence on stacking sequence.

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Kin Fai Mak¹, Jie Shan², Tony F. Heinz¹•Institutions (2)

Columbia University¹, Case Western Reserve University²

29 Apr 2010-Physical Review Letters

TL;DR: The electronic structure of few-layer graphene (FLG) samples with crystalline order was investigated experimentally by infrared absorption spectroscopy for photon energies ranging from 0.2-1 eV to demonstrate the pronounced effect of stacking order on the electronic structure.

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Abstract: The electronic structure of few-layer graphene (FLG) samples with crystalline order was investigated experimentally by infrared absorption spectroscopy for photon energies ranging from 0.2-1 eV. Distinct optical conductivity spectra were observed for different samples having precisely the same number of layers. The different spectra arise from the existence of two stable polytypes of FLG, namely, Bernal (AB) stacking and rhombohedral (ABC) stacking. The observed absorption features, reflecting the underlying symmetry of the two polytypes and the nature of the associated van Hone singularities, were reproduced by explicit calculations within a tight-binding model. The findings demonstrate the pronounced effect of stacking order on the electronic structure of FLG.

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272 citations

Journal Article•DOI•

Plasmonics in Dirac systems: from graphene to topological insulators

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Tobias Stauber

26 Mar 2014-Journal of Physics: Condensed Matter

TL;DR: Deep intrinsic plasmon excitation of single and bilayer graphene via hydrodynamic equations and the random phase approximation is discussed and a comprehensive introduction to the standard models and techniques is given.

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Abstract: Recent developments in the emerging field of plasmonics in graphene and other Dirac systems are reviewed and a comprehensive introduction to the standard models and techniques is given. In particular, we discuss intrinsic plasmon excitation of single-?and bilayer graphene via hydrodynamic equations and the random phase approximation, but also comment on double and multilayer structures. Additionally, we address Dirac systems in the retardation limit and also with large spin?orbit coupling including topological insulators. Finally, we summarize basic properties of the charge, current and photon linear response functions in an appendix.

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272 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

25 Nov 2016-arXiv: Mesoscale and Nanoscale Physics

TL;DR: In this article, a review of the state of the art in strain and ripple-induced effects on the electronic and optical properties of graphene is presented, with a focus on the Raman spectrum.

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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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271 citations

Journal Article•DOI•

Recent advances in two-dimensional-material-based sensing technology toward health and environmental monitoring applications

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Deepika Tyagi¹, Huide Wang¹, Weichun Huang², Lanping Hu², Yanfeng Tang², Zhinan Guo¹, Zhengbiao Ouyang¹, Han Zhang¹ - Show less +4 more•Institutions (2)

Shenzhen University¹, Nantong University²

13 Feb 2020-Nanoscale

TL;DR: 2D-nanomaterial-based electrochemical sensors that can be used to check for contaminations from heavy metals, organic/inorganic compounds, poisonous gases, pesticides, bacteria, antibiotics, etc., in water or air, which are severe risks to human wellbeing as well as the environment are highlighted.

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Abstract: Monitoring harmful and toxic chemicals, gases, microorganisms, and radiation has been a challenge to the scientific community for the betterment of human health and environment. Two-dimensional (2D)-material-based sensors are highly efficient and compatible with modern fabrication technology, which yield data that can be proficiently used for health and environmental monitoring. Graphene and its oxides, black phosphorus (BP), transition metal dichalcogenides (TMDCs), metal oxides, and other 2D nanomaterials have demonstrated properties that have been alluring for the manufacture of highly sensitive sensors due to their unique material properties arising from their inherent structures. This review summarizes the properties of 2D nanomaterials that can provide a platform to develop high-performance sensors. In this review, we have also discussed the advances made in the field of infrared photodetectors and electrochemical sensors and how the structural properties of 2D nanomaterials affect sensitivity and performance. Further, this review highlights 2D-nanomaterial-based electrochemical sensors that can be used to check for contaminations from heavy metals, organic/inorganic compounds, poisonous gases, pesticides, bacteria, antibiotics, etc., in water or air, which are severe risks to human wellbeing as well as the environment. Moreover, the limitations, future prospects, and challenges for the development of sensors based on 2D materials are also discussed for future advancements.

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269 citations

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References

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Journal Article•DOI•

Electric Field Effect in Atomically Thin Carbon Films

[...]

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)....
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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....
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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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