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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
21 Feb 2014-Science
TL;DR: In this article, 3D Dirac fermions with linear dispersions along all momentum directions were detected in 3D topological Dirac semimetals (TDSs) with angle-resolved photoemission spectroscopy.
Abstract: Three-dimensional (3D) topological Dirac semimetals (TDSs) represent an unusual state of quantum matter that can be viewed as “3D graphene.” In contrast to 2D Dirac fermions in graphene or on the surface of 3D topological insulators, TDSs possess 3D Dirac fermions in the bulk. By investigating the electronic structure of Na 3 Bi with angle-resolved photoemission spectroscopy, we detected 3D Dirac fermions with linear dispersions along all momentum directions. Furthermore, we demonstrated the robustness of 3D Dirac fermions in Na 3 Bi against in situ surface doping. Our results establish Na 3 Bi as a model system for 3D TDSs, which can serve as an ideal platform for the systematic study of quantum phase transitions between rich topological quantum states.

1,920 citations

Journal ArticleDOI
TL;DR: In this paper, the authors review the recent progress and challenges of 2D van der Waals interactions and offer a perspective on the exploration of 2DLM-based vdWHs for future application in electronics and optoelectronics.
Abstract: Two-dimensional layered materials (2DLMs) have been a central focus of materials research since the discovery of graphene just over a decade ago. Each layer in 2DLMs consists of a covalently bonded, dangling-bond-free lattice and is weakly bound to neighbouring layers by van der Waals interactions. This makes it feasible to isolate, mix and match highly disparate atomic layers to create a wide range of van der Waals heterostructures (vdWHs) without the constraints of lattice matching and processing compatibility. Exploiting the novel properties in these vdWHs with diverse layering of metals, semiconductors or insulators, new designs of electronic devices emerge, including tunnelling transistors, barristors and flexible electronics, as well as optoelectronic devices, including photodetectors, photovoltaics and light-emitting devices with unprecedented characteristics or unique functionalities. We review the recent progress and challenges, and offer our perspective on the exploration of 2DLM-based vdWHs for future application in electronics and optoelectronics. With a dangling-bond-free surface, two dimensional layered materials (2DLMs) can enable the creation of diverse van der Waals heterostructures (vdWHs) without the conventional constraint of lattice matching or process compatibility. This Review discusses the recent advances in exploring 2DLM vdWHs for future electronics and optoelectronics.

1,850 citations

Journal ArticleDOI
05 Jul 2012-Nature
TL;DR: Using infrared nano-imaging, it is shown that common graphene/SiO2/Si back-gated structures support propagating surface plasmons and changes both the amplitude and the wavelength are altered by varying the gate voltage.
Abstract: Surface plasmons are collective oscillations of electrons in metals or semiconductors that enable confinement and control of electromagnetic energy at subwavelength scales. Rapid progress in plasmonics has largely relied on advances in device nano-fabrication, whereas less attention has been paid to the tunable properties of plasmonic media. One such medium--graphene--is amenable to convenient tuning of its electronic and optical properties by varying the applied voltage. Here, using infrared nano-imaging, we show that common graphene/SiO(2)/Si back-gated structures support propagating surface plasmons. The wavelength of graphene plasmons is of the order of 200 nanometres at technologically relevant infrared frequencies, and they can propagate several times this distance. We have succeeded in altering both the amplitude and the wavelength of these plasmons by varying the gate voltage. Using plasmon interferometry, we investigated losses in graphene by exploring real-space profiles of plasmon standing waves formed between the tip of our nano-probe and the edges of the samples. Plasmon dissipation quantified through this analysis is linked to the exotic electrodynamics of graphene. Standard plasmonic figures of merit of our tunable graphene devices surpass those of common metal-based structures.

1,849 citations

Journal ArticleDOI
05 Jul 2012-Nature
TL;DR: A successful alliance between nanoelectronics and nano-optics enables the development of active subwavelength-scale optics and a plethora of nano-optoelectronic devices and functionalities, such as tunable metamaterials, nanoscale optical processing, and strongly enhanced light–matter interactions for quantum devices and biosensing applications.
Abstract: The ability to manipulate optical fields and the energy flow of light is central to modern information and communication technologies, as well as quantum information processing schemes However, because photons do not possess charge, a way of controlling them efficiently by electrical means has so far proved elusive A promising way to achieve electric control of light could be through plasmon polaritons—coupled excitations of photons and charge carriers—in graphene In this two-dimensional sheet of carbon atoms, it is expected that plasmon polaritons and their associated optical fields can readily be tuned electrically by varying the graphene carrier density Although evidence of optical graphene plasmon resonances has recently been obtained spectroscopically, no experiments so far have directly resolved propagating plasmons in real space Here we launch and detect propagating optical plasmons in tapered graphene nanostructures using near-field scattering microscopy with infrared excitation light We provide real-space images of plasmon fields, and find that the extracted plasmon wavelength is very short—more than 40 times smaller than the wavelength of illumination We exploit this strong optical field confinement to turn a graphene nanostructure into a tunable resonant plasmonic cavity with extremely small mode volume The cavity resonance is controlled in situ by gating the graphene, and in particular, complete switching on and off of the plasmon modes is demonstrated, thus paving the way towards graphene-based optical transistors This successful alliance between nanoelectronics and nano-optics enables the development of active subwavelength-scale optics and a plethora of nano-optoelectronic devices and functionalities, such as tunable metamaterials, nanoscale optical processing, and strongly enhanced light–matter interactions for quantum devices and biosensing applications

1,845 citations

Journal ArticleDOI
02 May 2012-ACS Nano
TL;DR: The latest progress in graphene photonics, plasmonics, and broadband optoelectronic devices is reviewed, with particular emphasis on the ability to integrate graphenePhotonics onto the silicon platform to afford broadband operation in light routing and amplification.
Abstract: Graphene has been hailed as a wonderful material in electronics, and recently, it is the rising star in photonics, as well. The wonderful optical properties of graphene afford multiple functions of signal emitting, transmitting, modulating, and detection to be realized in one material. In this paper, the latest progress in graphene photonics, plasmonics, and broadband optoelectronic devices is reviewed. Particular emphasis is placed on the ability to integrate graphene photonics onto the silicon platform to afford broadband operation in light routing and amplification, which involves components like polarizer, modulator, and photodetector. Other functions like saturable absorber and optical limiter are also reviewed.

1,778 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