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Journal ArticleDOI

The electronic properties of graphene

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.
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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Citations
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Journal ArticleDOI
TL;DR: In this article, a basic N-methyl-2-pyrrolidone (NMP) liquid exfoliation method is described to produce phosphorene with excellent water stability, controllable size and layer number, as well as in high yield.
Abstract: Although phosphorene has attracted much attention in electronics and optoelectronics as a new type of two-dimensional material, in-depth investigations and applications have been limited by the current synthesis techniques. Herein, a basic N-methyl-2-pyrrolidone (NMP) liquid exfoliation method is described to produce phosphorene with excellent water stability, controllable size and layer number, as well as in high yield. Phosphorene samples composed of one to four layers exhibit layer-dependent Raman scattering characteristics thus providing a fast and efficient means for the in situ determination of the thickness (layer number) of phosphorene. The linear and nonlinear ultrafast absorption behavior of the as-exfoliated phosphorene is investigated systematically by UV–vis–NIR absorption and Z-scan measurements. By taking advantage of their unique nonlinear absorption, ultrashort pulse generation applicable to optical saturable absorbers is demonstrated. In addition to a unique fabrication technique, our work also reveals the large potential of phosphorene in ultrafast photonics.

820 citations

Journal ArticleDOI
TL;DR: The results demonstrate that atomically thin h-BN acts as a defect-free dielectric with a high breakdown field and offers great potential for applications in tunnel devices and in field-effect transistors with ahigh carrier density in the conducting channel.
Abstract: We investigate the electronic properties of ultrathin hexagonal boron nitride (h-BN) crystalline layers with different conducting materials (graphite, graphene, and gold) on either side of the barrier layer. The tunnel current depends exponentially on the number of h-BN atomic layers, down to a monolayer thickness. Conductive atomic force microscopy scans across h-BN terraces of different thickness reveal a high level of uniformity in the tunnel current. Our results demonstrate that atomically thin h-BN acts as a defect-free dielectric with a high breakdown field. It offers great potential for applications in tunnel devices and in field-effect transistors with a high carrier density in the conducting channel.

812 citations

Journal ArticleDOI
TL;DR: Two-probe and van der Pauw electrical measurements reveal bulk and surface conductivity values of 2 and 40 S·cm(-1), respectively, both records for MOFs and among the best for any coordination polymer.
Abstract: Reaction of 2,3,6,7,10,11-hexaaminotriphenylene with Ni2+ in aqueous NH3 solution under aerobic conditions produces Ni3(HITP)2 (HITP = 2,3,6,7,10,11-hexaiminotriphenylene), a new two-dimensional metal–organic framework (MOF). The new material can be isolated as a highly conductive black powder or dark blue-violet films. Two-probe and van der Pauw electrical measurements reveal bulk (pellet) and surface (film) conductivity values of 2 and 40 S·cm–1, respectively, both records for MOFs and among the best for any coordination polymer.

809 citations

Journal ArticleDOI
TL;DR: This work shows that by employing accidental degeneracy, dielectric photonic crystals can be designed and fabricated that exhibit Dirac cone dispersion at the centre of the Brillouin zone at a finite frequency and numerically and experimentally demonstrates in the microwave regime that these crystals manipulate waves as if they had near-zero refractive indices at and near the Dirac point frequency.
Abstract: A zero-refractive-index metamaterial is one in which waves do not experience any spatial phase change, and such a peculiar material has many interesting wave-manipulating properties. These materials can in principle be realized using man-made composites comprising metallic resonators or chiral inclusions, but metallic components have losses that compromise functionality at high frequencies. It would be highly desirable if we could achieve a zero refractive index using dielectrics alone. Here, we show that by employing accidental degeneracy, dielectric photonic crystals can be designed and fabricated that exhibit Dirac cone dispersion at the centre of the Brillouin zone at a finite frequency. In addition to many interesting properties intrinsic to a Dirac cone dispersion, we can use effective medium theory to relate the photonic crystal to a material with effectively zero permittivity and permeability. We then numerically and experimentally demonstrate in the microwave regime that such dielectric photonic crystals with reasonable dielectric constants manipulate waves as if they had near-zero refractive indices at and near the Dirac point frequency.

806 citations

Journal ArticleDOI
TL;DR: Graphene has been attracting enormous attention in the scientific community as discussed by the authors, since the demonstration of its easy isolation by the exfoliation of graphite in 2004 by Novoselov, Geim and co-workers.

798 citations

References
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Journal ArticleDOI
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.
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.

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 ArticleDOI
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.
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.

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
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.
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

20,724 citations

Journal ArticleDOI
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.
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.

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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Book
01 Jan 1939

14,299 citations