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•

Dielectric properties of hexagonal boron nitride and transition metal dichalcogenides: from monolayer to bulk

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Akash Laturia¹, Maarten L. Van de Put¹, William G. Vandenberghe¹•Institutions (1)

University of Texas at Dallas¹

08 Mar 2018

TL;DR: In this article, the out-of-plane and in-plane dielectric response of TMDs in trigonal prismatic and octahedral coordination, as well as for hexagonal boron nitride (h-BN) with a thickness ranging from monolayer and bilayer to bulk, was analyzed.

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Abstract: Hexagonal boron nitride (h-BN) and semiconducting transition metal dichalcogenides (TMDs) promise greatly improved electrostatic control in future scaled electronic devices. To quantify the prospects of these materials in devices, we calculate the out-of-plane and in-plane dielectric constant from first principles for TMDs in trigonal prismatic and octahedral coordination, as well as for h-BN, with a thickness ranging from monolayer and bilayer to bulk. Both the ionic and electronic contribution to the dielectric response are computed. Our calculations show that the out-of-plane dielectric response for the transition-metal dichalcogenides is dominated by its electronic component and that the dielectric constant increases with increasing chalcogen atomic number. Overall, the out-of-plane dielectric constant of the TMDs and h-BN increases by less than 15% as the number of layers is increased from monolayer to bulk, while the in-plane component remains unchanged. Our computations also reveal that for octahedrally coordinated TMDs the ionic (static) contribution to the dielectric response is very high (4.5 times the electronic contribution) in the in-plane direction. This indicates that semiconducting TMDs in the tetragonal phase will suffer from excessive polar-optical scattering thereby deteriorating their electronic transport properties. The out-of-plane dielectric constant of transition metal dichalcogenides and h-BN is thickness-dependent, unlike their in-plane counterpart. A team led by William Vandenberghe at the University of Texas at Dallas performed calculations of the optical and static relative permittivity of free-standing monolayer, bilayer, and bulk transition metal dichalcogenides, in the in-plane and out-of-plane directions. In h-BN, the in-plane contribution was found to be larger than its out-of-plane counterpart, and independent on the number of h-BN layers. Conversely, the out-of-plane h-BN dielectric constant showed an increase when going from monolayer to bulk. In transition metal dichalcogenides, the dielectric constant components displayed similar trends to those observed in h-BN with regards to their thickness evolution. The calculations also indicated that the electronic component dominates the overall dielectric response for most of the analyzed 2D materials.

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585 citations

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

...However, since graphene does not have a band-gap, it is not well suited for digital electronics applications.(1) Consequently, significant research effort has been directed toward 2D semiconductors....
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Journal Article•DOI•

Design, Synthesis, and Characterization of Graphene–Nanoparticle Hybrid Materials for Bioapplications

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Perry T. Yin¹, Shreyas Shah¹, Manish Chhowalla¹, Ki-Bum Lee¹•Institutions (1)

Rutgers University¹

18 Feb 2015-Chemical Reviews

TL;DR: Graphene nanoparticle hybrids exist in two forms, as graphene–nanoparticle composites and graphene-encapsulated nanoparticles, and can be used for various bioapplications including biosensors, photothermal therapies, stem cell/tissue engineering, drug/gene delivery, and bioimaging.

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Abstract: Graphene is composed of single-atom thick sheets of sp2 bonded carbon atoms that are arranged in a perfect two-dimensional (2D) honeycomb lattice. Because of this structure, graphene is characterized by a number of unique and exceptional structural, optical, and electronic properties.1 Specifically, these extraordinary properties include, but are not limited to, a high planar surface area that is calculated to be 2630 m2 g−1,2 superior mechanical strength with a Young’s modulus of 1100 GPa,3 unparalleled thermal conductivity (5000 W m−1 K−1),4 remarkable electronic properties (e.g., high carrier mobility [10 000 cm2 V−1 s−1] and capacity),5 and alluring optical characteristics (e.g., high opacity [~97.7%] and the ability to quench fluorescence).6 As such, it should come as no surprise that graphene is currently, without any doubt, the most intensively studied material for a wide range of applications that include electronic, energy, and sensing outlets.1c Moreover, because of these unique chemical and physical properties, graphene and graphene-based nanomaterials have attracted increasing interest, and, arguably, hold the greatest promise for implementation into a wide array of bioapplications.7 In the last several years, numerous studies have utilized graphene in bioapplications ranging from the delivery of chemotherapeutics for the treatment of cancer8 to biosensing applications for a host of medical conditions9 and even for the differentiation and imaging of stem cells.10 While promising and exciting, recent reports have demonstrated that the combination of graphene with nanomaterials such as nanoparticles, thereby forming graphene–nanoparticle hybrid structures, offers a number of additional unique physicochemical properties and functions that are both highly desirable and markedly advantageous for bioapplications when compared to the use of either material alone (Figure 1).11 These graphene–nanoparticle hybrid structures are especially alluring because not only do they display the individual properties of the nanoparticles, which can already possess beneficial optical, electronic, magnetic, and structural properties that are unavailable in bulk materials, and of graphene, but they also exhibit additional advantageous and often synergistic properties that greatly augment their potential for bioapplications. Open in a separate window Figure 1 Graphene nanoparticle hybrids exist in two forms, as graphene–nanoparticle composites and graphene-encapsulated nanoparticles, and can be used for various bioapplications including biosensors, photothermal therapies, stem cell/tissue engineering, drug/gene delivery, and bioimaging. Panel (A) reprinted with permission from ref 110. Copyright 2012 Wiley. Panel (B) reprinted with permission from ref 211. Copyright 2013 Elsevier. Panel (C) reprinted with permission from ref 244. Copyright 2013 Wiley.

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583 citations

Journal Article•DOI•

Chemical functionalization of graphene with defects.

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Danil W. Boukhvalov¹, Mikhail I. Katsnelson¹•Institutions (1)

Radboud University Nijmegen¹

29 Oct 2008-Nano Letters

TL;DR: In this article, the authors simulated a chemistry of imperfect graphene for a broad class of defects (Stone-Wales (SW) defects, bivacancies, nitrogen substitution impurities, and zigzag edges) by density functional calculations.

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Abstract: Defects change essentially not only the electronic properties but also the chemical properties of graphene, being centers of its chemical activity. Their functionalization is a way to modify the electronic and crystal structure of graphene, which may be important for graphene-based nanoelectronics. Using hydrogen as an example, we have simulated a chemistry of imperfect graphene for a broad class of defects (Stone-Wales (SW) defects, bivacancies, nitrogen substitution impurities, and zigzag edges) by density functional calculations. We have studied also an effect of finite width of graphene nanoribbons on their chemical properties. It is shown that magnetism at graphene edges is fragile, with respect to oxidation, and, therefore, chemical protection of the graphene edges may be required for the application of graphene in spintronics. At the same time, hydrogenation of the SW defects may be a prospective way to create magnetic carbon.

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582 citations

Journal Article•DOI•

Graphene synthesis: relationship to applications.

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Rebecca S. Edwards¹, Karl S. Coleman¹•Institutions (1)

Durham University¹

07 Jan 2013-Nanoscale

TL;DR: This review highlights the different methods available for the synthesis of graphene and discusses the viability and practicalities of using the materials produced via these methods for different graphene-based applications.

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Abstract: Graphene is a true wonder material that promises much in a variety of applications that include electronic devices, supercapacitors, batteries, composites, flexible transparent displays and sensors. This review highlights the different methods available for the synthesis of graphene and discusses the viability and practicalities of using the materials produced via these methods for different graphene-based applications.

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578 citations

Journal Article•DOI•

Z-scan measurement of the nonlinear refractive index of graphene.

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Han Zhang¹, Stéphane Virally², Qiaoliang Bao³, Loh Kian Ping³, Serge Massar¹, Nicolas Godbout², Pascal Kockaert¹ - Show less +3 more•Institutions (3)

Université libre de Bruxelles¹, École Polytechnique de Montréal², National University of Singapore³

01 Jun 2012-Optics Letters

TL;DR: It is found that the nonlinear refractive index decreases with increasing excitation flux but slower than the absorption, suggesting that graphene may be a very promising nonlinear medium, paving the way for graphene-based nonlinear photonics.

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Abstract: Under strong laser illumination, few-layer graphene exhibits both a transmittance increase due to saturable absorption and a nonlinear phase shift. Here, we unambiguously distinguish these two nonlinear optical effects and identify both real and imaginary parts of the complex nonlinear refractive index of graphene. We show that graphene possesses a giant nonlinear refractive index n2≃10−7 cm2 W−1, almost 9 orders of magnitude larger than bulk dielectrics. We find that the nonlinear refractive index decreases with increasing excitation flux but slower than the absorption. This suggests that graphene may be a very promising nonlinear medium, paving the way for graphene-based nonlinear photonics.

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578 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....
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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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