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•

Mechanical, Thermal, and Electrical Properties of Graphene-Epoxy Nanocomposites—A Review

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Rasheed Atif¹, Islam Shyha¹, Fawad Inam¹•Institutions (1)

Northumbria University¹

04 Aug 2016-Polymers

TL;DR: In this review, mechanical, thermal, and electrical properties of graphene reinforced epoxy nanocomposites will be correlated with the topographical features, morphology, weight fraction, dispersion state, and surface functionalization of graphene.

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Abstract: Monolithic epoxy, because of its brittleness, cannot prevent crack propagation and is vulnerable to fracture. However, it is well established that when reinforced—especially by nano-fillers, such as metallic oxides, clays, carbon nanotubes, and other carbonaceous materials—its ability to withstand crack propagation is propitiously improved. Among various nano-fillers, graphene has recently been employed as reinforcement in epoxy to enhance the fracture related properties of the produced epoxy–graphene nanocomposites. In this review, mechanical, thermal, and electrical properties of graphene reinforced epoxy nanocomposites will be correlated with the topographical features, morphology, weight fraction, dispersion state, and surface functionalization of graphene. The factors in which contrasting results were reported in the literature are highlighted, such as the influence of graphene on the mechanical properties of epoxy nanocomposites. Furthermore, the challenges to achieving the desired performance of polymer nanocomposites are also suggested throughout the article.

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241 citations

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

...The Fermi level in undoped graphene lies at the Dirac point, where the inimum conductivity values are achieved [197]....
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...The Fermi level in undoped graphene lies at the Dirac point, where the minimum conductivity values are achieved [197]....
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Journal Article•DOI•

Dynamics of single Fe atoms in graphene vacancies.

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Alex W. Robertson¹, B. Montanari², Kuang He¹, Judy S. Kim¹, Christopher S. Allen¹, Yimin A. Wu¹, Jaco Olivier³, J.H. Neethling³, Nicholas M. Harrison², Angus I. Kirkland¹, Jamie H. Warner¹ - Show less +7 more•Institutions (3)

University of Oxford¹, Rutherford Appleton Laboratory², Nelson Mandela Metropolitan University³

21 Mar 2013-Nano Letters

TL;DR: It is found that the incorporation of a dopant atom results in pronounced displacements of the surrounding carbon atoms of up to 0.5 Å, which is in good agreement with density functional theory calculations.

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Abstract: Focused electron beam irradiation has been used to create mono and divacancies in graphene within a defined area, which then act as trap sites for mobile Fe atoms initially resident on the graphene surface. Aberration-corrected transmission electron microscopy at 80 kV has been used to study the real time dynamics of Fe atoms filling the vacancy sites in graphene with atomic resolution. We find that the incorporation of a dopant atom results in pronounced displacements of the surrounding carbon atoms of up to 0.5 A, which is in good agreement with density functional theory calculations. Once incorporated into the graphene lattice, Fe atoms can transition to adjacent lattice positions and reversibly switch their bonding between four and three nearest neighbors. The C atoms adjacent to the Fe atoms are found to be more susceptible to Stone-Wales type bond rotations with these bond rotations associated with changes in the dopant bonding configuration. These results demonstrate the use of controlled electron ...

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241 citations

Journal Article•DOI•

Black phosphorus a new saturable absorber material for ultrashort pulse generation

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Jaroslaw Sotor¹, Grzegorz Sobon, W. Macherzyński, Piotr Paletko, Krzysztof M. Abramski - Show less +1 more•Institutions (1)

Wrocław University of Technology¹

18 Apr 2015-arXiv: Materials Science

TL;DR: In this paper, a broadband saturable absorber of black phosphorus was used for ultrashort optical pulse generation, where the mechanically exfoliated ~300 nm thick layers were transferred onto the fiber core and under pulsed excitation at 1560 nm wavelength its transmission increases by 4.4%.

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Abstract: Low-dimensional materials, due to their versatile properties are very interesting for numerous electronics and optoelectronics applications. Recently rediscovered black phosphorus, with a graphite-like structure can be exfoliated up to the single atomic layer. In contrary to graphene it possesses a direct band gap controllable by the number of stacked atomic layers. For those reasons, it is now intensively investigated. Here we demonstrate, that black phosphorus can serve as a broadband saturable absorber and can be used for ultrashort optical pulse generation. The mechanically exfoliated ~300 nm thick layers of black phosphorus were transferred onto the fiber core and under pulsed excitation at 1560 nm wavelength its transmission increases by 4.4%. It was used to generate 272 fs-short pulses at 1550 nm and 739 fs at 1910 nm. The obtained results shows that black phosphorus can be effectively used for ultrashort pulse generation and proves its great potential to future applications.

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241 citations

Book Chapter•DOI•

Condensed Matter and AdS/CFT

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Subir Sachdev¹•Institutions (1)

Harvard University¹

16 Feb 2010-Lecture Notes in Physics

TL;DR: In this paper, a review of strong coupling problems in condensed matter physics is presented, and insights gained by application of the AdS/CFT correspondence are discussed. But the authors do not consider the problem of symmetry breaking transitions of two-dimensional systems in the presence of gapless electronic excitations at isolated points or along lines.

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Abstract: I review two classes of strong coupling problems in condensed matter physics, and describe insights gained by application of the AdS/CFT correspondence. The first class concerns non-zero temperature dynamics and transport in the vicinity of quantum critical points described by relativistic field theories. I describe how relativistic structures arise in models of physical interest, present results for their quantum critical crossover functions and magneto-thermoelectric hydrodynamics. The second class concerns symmetry breaking transitions of two-dimensional systems in the presence of gapless electronic excitations at isolated points or along lines (i.e. Fermi surfaces) in the Brillouin zone. I describe the scaling structure of a recent theory of the Ising-nematic transition in metals, and discuss its possible connection to theories of Fermi surfaces obtained from simple AdS duals.

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240 citations

Journal Article•DOI•

Graphite and Hexagonal Boron-Nitride Possess the Same Interlayer Distance. Why?

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Oded Hod

17 Sep 2011-arXiv: Materials Science

TL;DR: The conclusions drawn here regarding the role of electrostatic interactions between partially charged atomic centers for the interlayer binding of h-BN are of a general nature and are expected to hold true for many other polar layered systems.

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Abstract: Graphite and hexagonal boron nitride (h-BN) are two prominent members of the family of layered materials possessing a hexagonal lattice. While graphite has non-polar homo-nuclear C-C intra-layer bonds, h-BN presents highly polar B-N bonds resulting in different optimal stacking modes of the two materials in bulk form. Furthermore, the static polarizabilities of the constituent atoms considerably differ from each other suggesting large differences in the dispersive component of the interlayer bonding. Despite these major differences both materials present practically identical interlayer distances. To understand this finding, a comparative study of the nature of the interlayer bonding in both materials is presented. A full lattice sum of the interactions between the partially charged atomic centers in h-BN results in vanishingly small monopolar electrostatic contributions to the interlayer binding energy. Higher order electrostatic multipoles, exchange, and short-range correlation contributions are found to be very similar in both materials and to almost completely cancel out by the Pauli repulsions at physically relevant interlayer distances resulting in a marginal effective contribution to the interlayer binding. Further analysis of the dispersive energy term reveals that despite the large differences in the individual atomic polarizabilities the hetero-atomic B-N C6 coefficient is very similar to the homo-atomic C-C coefficient in the hexagonal bulk form resulting in very similar dispersive contribution to the interlayer binding. The overall binding energy curves of both materials are thus very similar predicting practically the same interlayer distance and very similar binding energies.

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240 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....
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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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