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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 free-standing, large-scale nanoporous graphene with 2D electronic properties and high electron mobility holds great promise for practical applications in 3D electronic devices.
Abstract: We report three-dimensional (3D) nanoporous graphene with preserved 2D electronic properties, tunable pore sizes, and high electron mobility for electronic applications. The complex 3D network comprised of interconnected graphene retains a 2D coherent electron system of massless Dirac fermions. The transport properties of the nanoporous graphene show a semiconducting behavior and strong pore-size dependence, together with unique angular independence. The free-standing, large-scale nanoporous graphene with 2D electronic properties and high electron mobility holds great promise for practical applications in 3D electronic devices.

228 citations

Journal ArticleDOI
TL;DR: This work finds that pseudohalogen (CN and OCN) passivated PNRs not only show desired VBM and CBM band edge positions induced by edge electric dipole layer, but also possess intrinsic optoelectronic properties of phosphorene, for both water oxidation and hydrogen reduction in photocatalytic water splitting without using extra energy.
Abstract: Two-dimensional phosphorene with desirable optoelectronic properties (ideal band gap, high carrier mobility, and strong visible light absorption) is a promising metal-free photocatalyst for water splitting. However, the band edge positions of the valence band maximum (VBM) and conduction band maximum (CBM) of phosphorene are higher than the redox potentials in photocatalytic water splitting reactions. Thus, phosphorene can only be used as the photocathode for hydrogen evolution reaction as a low-efficiency visible-light-driven photocatalyst for hydrogen production in solar water splitting cells. Here, we propose a new mechanism to improve the photocatalytic efficiency of phosphorene nanoribbons (PNRs) by modifying their edges for full reactions in photocatalytic water splitting. By employing first-principles density functional theory calculations, we find that pseudohalogen (CN and OCN) passivated PNRs not only show desired VBM and CBM band edge positions induced by edge electric dipole layer, but also po...

228 citations

Journal ArticleDOI
TL;DR: Self-assembly of various phthalocyanine molecules and a derivative on an epitaxial graphene monolayer has been investigated by means of in situ ultrahigh vacuum scanning tunneling microscopy, demonstrating that MG can act as a wonderful template for the fabrication of unique nanoarchitectures with remarkable properties.
Abstract: Self-assembly of various phthalocyanine (Pc) molecules and a derivative on an epitaxial graphene monolayer (MG) has been investigated by means of in situ ultrahigh vacuum scanning tunneling microscopy. The formation of regular Kagome lattices that duplicate the lattice of the moire pattern of MG was observed, demonstrating that MG can act as a wonderful template for the fabrication of unique nanoarchitectures with remarkable properties. Varying the central metal ion of the Pc molecule affords Kagome lattices with tunable molecular spins, providing ideal two-dimensional model systems for studying frustration physics.

228 citations

Journal ArticleDOI
TL;DR: Electrochemical exfoliation of graphite allowed the formation of highly oxidized graphene with a C/O ratio close to 4.0 and represents a possible avenue for the mass production of graphene oxide as valid alternative to the current laborious and dangerous chemical procedures, which also have limited scalability.
Abstract: Top-down methods are of key importance for large-scale graphene and graphene oxide preparation. Electrochemical exfoliation of graphite has lately gained much interest because of the simplicity of execution, the short process time, and the good quality of graphene that can be obtained. Here, we test three different electrolytes, that is, H2 SO4 , Na2 SO4 , and LiClO4 , with a common exfoliation procedure to evaluate the difference in structural and chemical properties that result for the graphene. The properties are analyzed by means of scanning transmission electron microscopy (STEM), Raman spectroscopy, and X-ray photoelectron spectroscopy. We then tested the graphene materials for electrochemical applications, measuring the heterogeneous electron transfer (HET) rates with a Fe(CN)6 (3-/4-) redox probe, and their capacitive behavior in alkaline solutions. We correlate the electrochemical features with the presence of structural defects and oxygen functionalities on the graphene materials. In particular, the use of LiClO4 during the electrochemical exfoliation of graphite allowed the formation of highly oxidized graphene with a C/O ratio close to 4.0 and represents a possible avenue for the mass production of graphene oxide as valid alternative to the current laborious and dangerous chemical procedures, which also have limited scalability.

228 citations

Journal ArticleDOI
TL;DR: Graphene and graphene oxide composites have been used for wastewater purification because of their adsorption, oxidation, and catalytic properties as mentioned in this paper, and their composites naturally have significant pore volume, high conductivity, rich surface chemistry, and an exceptionally large aspect ratio.
Abstract: Graphene, graphene oxide (GO), and their composites have been prominently utilized for wastewater purification because of their adsorption, oxidation, and catalytic properties. Graphene and GO and its composites naturally have significant pore volume, high conductivity, rich surface chemistry, and an exceptionally large aspect ratio which make it favorable for adsorption and catalysis of organic pollutants from wastewater. The sheet-like, resonating, polyaromatic π-system of graphene subsidiaries play a significant role in π–π interactions, hydrogen bonding, and/or electrostatic interactions with organic pollutants that include dyes, pharmaceutical waste, and agricultural and industrial effluents whose base structure consists of notably reactive unsaturated aromatic rings and oxygen-rich functional groups. The adsorption capacities of pollutants have been widely researched and catalogued by considering the adsorption isotherm (Langmuir, Freundlich, Temkin, DR model) they fit, the kinetic models (pseudo-fi...

228 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