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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: The continuous tuning of the electronic structure of atomically thin MoS2 on flexible substrates by applying a uniaxial tensile strain demonstrates the potential of two-dimensional crystals for applications in flexible electronics and optoelectronics.
Abstract: We demonstrate the continuous tuning of the electronic structure of atomically thin MoS2 on flexible substrates by applying a uniaxial tensile strain. A redshift at a rate of ~70 meV per percent applied strain for direct gap transitions, and at a rate 1.6 times larger for indirect gap transitions, have been determined by absorption and photoluminescence spectroscopy. Our result, in excellent agreement with first principles calculations, demonstrates the potential of twodimensional crystals for applications in flexible electronics and optoelectronics.

730 citations

Journal ArticleDOI
TL;DR: The model proposed explains why it is so difficult to reduce the graphite oxide up to pure graphene, and evolution of the electronic structure ofgraphite oxide with the coverage change is investigated.
Abstract: Based on density functional calculations, optimized structures of graphite oxide are found for various coverages by oxygen and hydroxyl groups, as well as their ratio corresponding to the minimum of total energy. The model proposed describes well-known experimental results. In particular, it explains why it is so difficult to reduce the graphite oxide up to pure graphene. Evolution of the electronic structure of graphite oxide with the coverage change is investigated.

729 citations

Journal ArticleDOI
TL;DR: The results show the possibility of inducing a macroscopic ferrimagnetic state in multilayered graphene just by randomly removing single C atoms.
Abstract: Atomic vacancies have a strong impact in the mechanical, electronic, and magnetic properties of graphenelike materials. By artificially generating isolated vacancies on a graphite surface and measuring their local density of states on the atomic scale, we have shown how single vacancies modify the electronic properties of this graphenelike system. Our scanning tunneling microscopy experiments, complemented by tight-binding calculations, reveal the presence of a sharp electronic resonance at the Fermi energy around each single graphite vacancy, which can be associated with the formation of local magnetic moments and implies a dramatic reduction of the charge carriers' mobility. While vacancies in single layer graphene lead to magnetic couplings of arbitrary sign, our results show the possibility of inducing a macroscopic ferrimagnetic state in multilayered graphene just by randomly removing single C atoms.

727 citations

Journal ArticleDOI
07 Jan 2010-Nature
TL;DR: A proof-of-principle quantum simulation of the one-dimensional Dirac equation using a single trapped ion set to behave as a free relativistic quantum particle and study Zitterbewegung for different initial superpositions of positive- and negative-energy spinor states.
Abstract: The Dirac equation, proposed by Paul Dirac in 1928 to describe the behaviour of relativistic quantum particles, merges quantum mechanics with special relativity. A number of peculiar effects emerge from the equation, including a rapid quivering motion or 'Zitterbewegung', well established in theory but difficult to observe in real particles. Christian Roos and colleagues have developed a proof-of-principle quantum simulation of the Dirac equation using a single trapped ion set to behave as a free relativistic quantum particle. The high level of control of trapped-ion experimental parameters in this system makes it possible to simulate and study Zitterbewegung and other textbook examples of relativistic quantum physics. The Dirac equation successfully merges quantum mechanics with special relativity. It predicts some peculiar effects such as 'Zitterbewegung', an unexpected quivering motion of a free relativistic quantum particle. This and other predicted phenomena are key fundamental examples for understanding relativistic quantum effects, but are difficult to observe in real particles. Here, using a single trapped ion set to behave as a free relativistic quantum particle, a quantum simulation of the one-dimensional Dirac equation is demonstrated. The Dirac equation1 successfully merges quantum mechanics with special relativity. It provides a natural description of the electron spin, predicts the existence of antimatter2 and is able to reproduce accurately the spectrum of the hydrogen atom. The realm of the Dirac equation—relativistic quantum mechanics—is considered to be the natural transition to quantum field theory. However, the Dirac equation also predicts some peculiar effects, such as Klein’s paradox3 and ‘Zitterbewegung’, an unexpected quivering motion of a free relativistic quantum particle4. These and other predicted phenomena are key fundamental examples for understanding relativistic quantum effects, but are difficult to observe in real particles. In recent years, there has been increased interest in simulations of relativistic quantum effects using different physical set-ups5,6,7,8,9,10,11, in which parameter tunability allows access to different physical regimes. Here we perform a proof-of-principle quantum simulation of the one-dimensional Dirac equation using a single trapped ion7 set to behave as a free relativistic quantum particle. We measure the particle position as a function of time and study Zitterbewegung for different initial superpositions of positive- and negative-energy spinor states, as well as the crossover from relativistic to non-relativistic dynamics. The high level of control of trapped-ion experimental parameters makes it possible to simulate textbook examples of relativistic quantum physics.

726 citations


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

  • ...Graphene is studied widely in connection to the Dirac equation [16, 17, 18]....

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Journal ArticleDOI
TL;DR: Recently, due to the attractive properties such as appropriate band structure, ultrahigh specific surface area, and more exposed active sites, two-dimensional (2D) photocatalysts have attracted significant attention as discussed by the authors.
Abstract: Hydrogen generation from the direct splitting of water by photocatalysis is regarded as a promising and renewable solution for the energy crisis The key to realize this reaction is to find an efficient and robust photocatalyst that ideally makes use of the energy from sunlight Recently, due to the attractive properties such as appropriate band structure, ultrahigh specific surface area, and more exposed active sites, two-dimensional (2D) photocatalysts have attracted significant attention for photocatalytic water splitting This Review attempts to summarize recent progress in the fabrication and applications of 2D photocatalysts including graphene-based photocatalysts, 2D oxides, 2D chalcogenides, 2D carbon nitride, and some other emerging 2D materials for water splitting The construction strategies and characterization techniques for 2D/2D photocatalysts are summarized Particular attention has been paid to the role of 2D/2D interfaces in these 2D photocatalysts as the interfaces and heterojunctions a

717 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