The electronic properties of graphene

doi:10.1103/REVMODPHYS.81.109

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The electronic properties of graphene

Journal Article•DOI•

The electronic properties of graphene

A. H. Castro Neto¹, Francisco Guinea², Nuno M. R. Peres³, Kostya S. Novoselov⁴, Andre K. Geim⁴ - Show less +1 more•Institutions (4)

Boston University¹, Spanish National Research Council², University of Minho³, University of Manchester⁴

14 Jan 2009-Reviews of Modern Physics (American Physical Society)-Vol. 81, Iss: 1, pp 109-162

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.

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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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Journal Article•DOI•

Dirac materials

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Tim O. Wehling, Annica M. Black-Schaffer, Alexander V. Balatsky

22 May 2014-arXiv: Materials Science

TL;DR: A wide range of materials, such as d-wave superconductors, graphene, and topological insulators, share a fundamental similarity: their low-energy fermionic excitations behave as massless Dirac particles rather than fermions obeying the usual Schrodinger Hamiltonian as mentioned in this paper.

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Abstract: A wide range of materials, like d-wave superconductors, graphene, and topological insulators, share a fundamental similarity: their low-energy fermionic excitations behave as massless Dirac particles rather than fermions obeying the usual Schrodinger Hamiltonian This emergent behavior of Dirac fermions in condensed matter systems defines the unifying framework for a class of materials we call "Dirac materials'' In order to establish this class of materials, we illustrate how Dirac fermions emerge in multiple entirely different condensed matter systems and we discuss how Dirac fermions have been identified experimentally using electron spectroscopy techniques (angle-resolved photoemission spectroscopy and scanning tunneling spectroscopy) As a consequence of their common low-energy excitations, this diverse set of materials shares a significant number of universal properties in the low-energy (infrared) limit We review these common properties including nodal points in the excitation spectrum, density of states, specific heat, transport, thermodynamic properties, impurity resonances, and magnetic field responses, as well as discuss many-body interaction effects We further review how the emergence of Dirac excitations is controlled by specific symmetries of the material, such as time-reversal, gauge, and spin-orbit symmetries, and how by breaking these symmetries a finite Dirac mass is generated We give examples of how the interaction of Dirac fermions with their distinct real material background leads to rich novel physics with common fingerprints such as the suppression of back scattering and impurity-induced resonant states

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749 citations

Journal Article•DOI•

Classification of stable three-dimensional Dirac semimetals with nontrivial topology

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Bohm-Jung Yang¹, Naoto Nagaosa²•Institutions (2)

Global Alliance in Management Education¹, University of Tokyo²

15 Sep 2014-Nature Communications

TL;DR: A general framework to classify stable 3D Dirac SMs in systems having the time-reversal, inversion and uniaxial rotational symmetries is proposed and it is shown that there are two distinct classes of DiracSMs.

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Abstract: A three-dimensional (3D) Dirac semimetal (SM) is the 3D analogue of graphene having linear energy dispersion around Fermi points Owing to the nontrivial topology of electronic wave functions, the 3D Dirac SM shows nontrivial physical properties and hosts various exotic quantum states such as Weyl SMs and topological insulators under proper external conditions There are several kinds of Dirac SMs proposed theoretically and partly confirmed experimentally, but its unified picture is still missing Here we propose a general framework to classify stable 3D Dirac SMs in systems having the time-reversal, inversion and uniaxial rotational symmetries We show that there are two distinct classes of 3D Dirac SMs In one class, the Dirac SM possesses a single Dirac point (DP) at a time-reversal invariant momentum on the rotation axis Whereas the other class of Dirac SMs have a pair of DPs created by band inversion, and carry a quantized topological invariant

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747 citations

Journal Article•DOI•

Buckled Germanene Formation on Pt(111)

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Linfei Li¹, Shuangzan Lu¹, Jinbo Pan¹, Zhihui Qin¹, Yuqi Wang¹, Yeliang Wang¹, Gengyu Cao¹, Shixuan Du¹, Hong-Jun Gao¹ - Show less +5 more•Institutions (1)

Chinese Academy of Sciences¹

01 Jul 2014-Advanced Materials

TL;DR: The resulting high-quality germanenes enables researchers to explore the fundamentals of germanene and its potential applications.

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Abstract: Germanene, a 2D honeycomb lattice analogous to graphene, is fabricated on a Pt(111) surface. It exhibits a buckled configuration with a (3 x 3) superlattice coinciding with the substrate's (root 19 x root 19) superstructure. Covalent bonds exist throughout the germanene layer. The resulting high-quality germanene enables researchers to explore the fundamentals of germanene and its potential applications.

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746 citations

Journal Article•DOI•

Graphene: An Emerging Electronic Material

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Nathan O. Weiss¹, Hailong Zhou¹, Lei Liao¹, Yuan Liu¹, Shan Jiang¹, Yu Huang², Yu Huang¹, Xiangfeng Duan¹, Xiangfeng Duan² - Show less +5 more•Institutions (2)

University of California, Los Angeles¹, California NanoSystems Institute²

14 Nov 2012-Advanced Materials

TL;DR: The versatility of graphene-based devices goes beyond conventional transistor circuits and includes flexible and transparent electronics, optoelectronics, sensors, electromechanical systems, and energy technologies.

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Abstract: Graphene, a single layer of carbon atoms in a honeycomb lattice, offers a number of fundamentally superior qualities that make it a promising material for a wide range of applications, particularly in electronic devices. Its unique form factor and exceptional physical properties have the potential to enable an entirely new generation of technologies beyond the limits of conventional materials. The extraordinarily high carrier mobility and saturation velocity can enable a fast switching speed for radio-frequency analog circuits. Unadulterated graphene is a semi-metal, incapable of a true off-state, which typically precludes its applications in digital logic electronics without bandgap engineering. The versatility of graphene-based devices goes beyond conventional transistor circuits and includes flexible and transparent electronics, optoelectronics, sensors, electromechanical systems, and energy technologies. Many challenges remain before this relatively new material becomes commercially viable, but laboratory prototypes have already shown the numerous advantages and novel functionality that graphene provides.

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740 citations

Journal Article•DOI•

Thermal conductivity and thermal rectification in graphene nanoribbons: a molecular dynamics study.

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Jiuning Hu¹, Xiulin Ruan¹, Yong P. Chen¹•Institutions (1)

Purdue University¹

05 Jun 2009-Nano Letters

TL;DR: In this article, the thermal conductivity of symmetric and asymmetric graphene nanoribbons (GNRs) of several nanometers in size (up to ∼4 nm wide and ∼10 nm long) was calculated.

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Abstract: We have used molecular dynamics to calculate the thermal conductivity of symmetric and asymmetric graphene nanoribbons (GNRs) of several nanometers in size (up to ∼4 nm wide and ∼10 nm long). For symmetric nanoribbons, the calculated thermal conductivity (e.g., ∼2000 W/m-K at 400 K for a 1.5 nm × 5.7 nm zigzag GNR) is on the similar order of magnitude of the experimentally measured value for graphene. We have investigated the effects of edge chirality and found that nanoribbons with zigzag edges have appreciably larger thermal conductivity than nanoribbons with armchair edges. For asymmetric nanoribbons, we have found significant thermal rectification. Among various triangularly shaped GNRs we investigated, the GNR with armchair bottom edge and a vertex angle of 30° gives the maximal thermal rectification. We also studied the effect of defects and found that vacancies and edge roughness in the nanoribbons can significantly decrease the thermal conductivity. However, substantial thermal rectification is ob...

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732 citations

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References

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Journal Article•DOI•

Electric Field Effect in Atomically Thin Carbon Films

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Kostya S. Novoselov¹, Andre K. Geim¹, Sergey V. Morozov, Da Jiang¹, Y. Zhang¹, S. V. Dubonos, Irina V. Grigorieva¹, A. A. Firsov - Show less +4 more•Institutions (1)

University of Manchester¹

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.

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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.

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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....
[...]
...…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)....
[...]
...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 Article•DOI•

The rise of graphene

[...]

Andre K. Geim¹, Kostya S. Novoselov¹•Institutions (1)

University of Manchester¹

01 Mar 2007-Nature Materials

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.

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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.

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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....
[...]
...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....
[...]
...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•

Theory of elasticity

[...]

Stephen P. Timoshenko, James Norman Goodier

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.

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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

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20,724 citations

Journal Article•DOI•

Two-dimensional gas of massless Dirac fermions in graphene

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Kostya S. Novoselov¹, A. K. Geim¹, Sergey V. Morozov, Da Jiang¹, Mikhail I. Katsnelson², Irina V. Grigorieva¹, S. V. Dubonos, A. A. Firsov - Show less +4 more•Institutions (2)

University of Manchester¹, Radboud University Nijmegen²

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.

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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.

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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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