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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
01 Apr 2010-Carbon
TL;DR: In this paper, the evolution of the intensity ratio between the G band (1585 cm−1) and the disorder-induced D band (1345 cm −1) with ion dose is determined, providing a spectroscopy-based method to quantify the density of defects in graphene.

1,488 citations

Journal ArticleDOI
01 Jul 2010-Carbon
TL;DR: In this paper, the most promising and appealing properties of graphene are summarized from an exponentially growing literature, with a particular attention to matching production methods to characteristics and to applications, including the high carrier mobility value in suspended and annealed samples for electronic devices, the thickness-dependent optical transparency and, in the mechanical section, the high robustness and full integration of graphene in sensing device applications, emphasizing on the high potential of graphene not only as a post-silicon materials for CMOS device application but more ambitiously as a platform for post-CMOS molecular architecture in

1,467 citations


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

  • ...[8] Neto AHC, Guinea F, Peres NMR, Novoselov KS, Geim AK....

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  • ...In the presence of an external potential, a gap can be opened close to the K point.[8, 9] Further generalization of the perfect stacking results in graphite with alternating (ABAB, Bernal type) or staggered (ABCABC, rhombohedral type) arrangement depending on whether the lateral carbon atom shift changes direction from one layer to the next or not....

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  • ...[43] Although his result became a standard method for electron microscopy sample preparation, the condensed matter physicists who had already predicted a number of properties for graphite [8] remained unaware that the single-atom thick sheet had almost been isolated....

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  • ...For a detailed account of these specific topics, the Reader is invited to refer to the excellent recent review articles dedicated to these aspects of graphene.[7, 8, 154, 164-166] Along with the large electronic coherence length,...

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  • ...This resulted in the successive discovery of a Berry's phase or a Quantum Hall effect (QHE) with fourthly degenerated Landau levels due to K and K' valley and pseudo-spin degeneracy except for the zero Landau level which is only twice degenerated due to strict electron-hole symmetry near the Dirac point.[8, 139, 140, 153-155] Similarly, bilayer graphene exhibits a distinct behaviour resulting from the zero-gap parabolic dispersion with two extra bands available....

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Journal ArticleDOI
TL;DR: In this paper, a summary of chemical doping of graphene aimed at tuning the electronic properties of graphene is presented, which will be beneficial to designing high performance electronic devices based on chemically doped graphene.
Abstract: Recently, a lot of effort has been focused on improving the performance and exploring the electric properties of graphene. This article presents a summary of chemical doping of graphene aimed at tuning the electronic properties of graphene. p-Type and n-type doping of graphene achieved through surface transfer doping or substitutional doping and their applications based on doping are reviewed. Chemical doping for band gap tuning in graphene is also presented. It will be beneficial to designing high performance electronic devices based on chemically doped graphene.

1,447 citations

Journal ArticleDOI
TL;DR: Luminescence in the visible region, especially by clusters protected with proteins, with a large Stokes shift, has been used for various sensing applications, down to a few tens of molecules/ions, in air and water.
Abstract: Atomically precise pieces of matter of nanometer dimensions composed of noble metals are new categories of materials with many unusual properties. Over 100 molecules of this kind with formulas such as Au25(SR)18, Au38(SR)24, and Au102(SR)44 as well as Ag25(SR)18, Ag29(S2R)12, and Ag44(SR)30 (often with a few counterions to compensate charges) are known now. They can be made reproducibly with robust synthetic protocols, resulting in colored solutions, yielding powders or diffractable crystals. They are distinctly different from nanoparticles in their spectroscopic properties such as optical absorption and emission, showing well-defined features, just like molecules. They show isotopically resolved molecular ion peaks in mass spectra and provide diverse information when examined through multiple instrumental methods. Most important of these properties is luminescence, often in the visible–near-infrared window, useful in biological applications. Luminescence in the visible region, especially by clusters prot...

1,443 citations

Journal ArticleDOI
TL;DR: The distinct properties resulting from various dopants, different doping levels and configurations, and synergistic effects from co-dopants are emphasized, hoping to assist a better understanding of doped graphene materials.
Abstract: Heteroatom doping can endow graphene with various new or improved electromagnetic, physicochemical, optical, and structural properties. This greatly extends the arsenal of graphene materials and their potential for a spectrum of applications. Considering the latest developments, we comprehensively and critically discuss the syntheses, properties and emerging applications of the growing family of heteroatom-doped graphene materials. The advantages, disadvantages, and preferential doping features of current synthesis approaches are compared, aiming to provide clues for developing new and controllable synthetic routes. We emphasize the distinct properties resulting from various dopants, different doping levels and configurations, and synergistic effects from co-dopants, hoping to assist a better understanding of doped graphene materials. The mechanisms underlying their advantageous uses for energy storage, energy conversion, sensing, and gas storage are highlighted, aiming to stimulate more competent applications.

1,440 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