The electronic properties of graphene

doi:10.1103/REVMODPHYS.81.109

Home
/
Papers
/
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.

read less

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.

...read moreread less

Content maybe subject to copyright Report

Citations

PDF

Open Access

More filters

Journal Article•DOI•

Electronics and optoelectronics of two-dimensional transition metal dichalcogenides.

[...]

Qing Hua Wang¹, Kourosh Kalantar-zadeh², Andras Kis³, Jonathan N. Coleman⁴, Michael S. Strano¹ - Show less +1 more•Institutions (4)

Massachusetts Institute of Technology¹, RMIT University², École Polytechnique Fédérale de Lausanne³, Trinity College, Dublin⁴

01 Nov 2012-Nature Nanotechnology

TL;DR: This work reviews the historical development of Transition metal dichalcogenides, methods for preparing atomically thin layers, their electronic and optical properties, and prospects for future advances in electronics and optoelectronics.

...read moreread less

Abstract: Single-layer metal dichalcogenides are two-dimensional semiconductors that present strong potential for electronic and sensing applications complementary to that of graphene.

...read moreread less

13,348 citations

Journal Article•DOI•

Graphene: Status and Prospects

[...]

Andre K. Geim¹•Institutions (1)

University of Manchester¹

19 Jun 2009-Science

TL;DR: This review analyzes recent trends in graphene research and applications, and attempts to identify future directions in which the field is likely to develop.

...read moreread less

Abstract: Graphene is a wonder material with many superlatives to its name. It is the thinnest known material in the universe and the strongest ever measured. Its charge carriers exhibit giant intrinsic mobility, have zero effective mass, and can travel for micrometers without scattering at room temperature. Graphene can sustain current densities six orders of magnitude higher than that of copper, shows record thermal conductivity and stiffness, is impermeable to gases, and reconciles such conflicting qualities as brittleness and ductility. Electron transport in graphene is described by a Dirac-like equation, which allows the investigation of relativistic quantum phenomena in a benchtop experiment. This review analyzes recent trends in graphene research and applications, and attempts to identify future directions in which the field is likely to develop.

...read moreread less

12,117 citations

Journal Article•DOI•

Topological insulators and superconductors

[...]

Xiao-Liang Qi¹, Shou-Cheng Zhang²•Institutions (2)

University of California, Santa Barbara¹, Stanford University²

14 Oct 2011-Reviews of Modern Physics

TL;DR: Topological superconductors are new states of quantum matter which cannot be adiabatically connected to conventional insulators and semiconductors and are characterized by a full insulating gap in the bulk and gapless edge or surface states which are protected by time reversal symmetry.

...read moreread less

Abstract: Topological insulators are new states of quantum matter which cannot be adiabatically connected to conventional insulators and semiconductors. They are characterized by a full insulating gap in the bulk and gapless edge or surface states which are protected by time-reversal symmetry. These topological materials have been theoretically predicted and experimentally observed in a variety of systems, including HgTe quantum wells, BiSb alloys, and Bi2Te3 and Bi2Se3 crystals. Theoretical models, materials properties, and experimental results on two-dimensional and three-dimensional topological insulators are reviewed, and both the topological band theory and the topological field theory are discussed. Topological superconductors have a full pairing gap in the bulk and gapless surface states consisting of Majorana fermions. The theory of topological superconductors is reviewed, in close analogy to the theory of topological insulators.

...read moreread less

11,092 citations

Journal Article•DOI•

Graphene and Graphene Oxide: Synthesis, Properties, and Applications

[...]

Yanwu Zhu¹, Shanthi Murali¹, Weiwei Cai¹, Xuesong Li¹, Ji Won Suk¹, Jeffrey R. Potts¹, Rodney S. Ruoff¹ - Show less +3 more•Institutions (1)

University of Texas at Austin¹

15 Sep 2010-Advanced Materials

TL;DR: An overview of the synthesis, properties, and applications of graphene and related materials (primarily, graphite oxide and its colloidal suspensions and materials made from them), from a materials science perspective.

...read moreread less

Abstract: There is intense interest in graphene in fields such as physics, chemistry, and materials science, among others. Interest in graphene's exceptional physical properties, chemical tunability, and potential for applications has generated thousands of publications and an accelerating pace of research, making review of such research timely. Here is an overview of the synthesis, properties, and applications of graphene and related materials (primarily, graphite oxide and its colloidal suspensions and materials made from them), from a materials science perspective.

...read moreread less

8,919 citations

Journal Article•DOI•

The chemistry of two-dimensional layered transition metal dichalcogenide nanosheets

[...]

Manishkumar Chhowalla¹, Hyeon Suk Shin², Goki Eda³, Lain-Jong Li⁴, Kian Ping Loh³, Hua Zhang⁵ - Show less +2 more•Institutions (5)

Rutgers University¹, Ulsan National Institute of Science and Technology², National University of Singapore³, Academia Sinica⁴, Nanyang Technological University⁵

01 Apr 2013-Nature Chemistry

TL;DR: This Review describes how the tunable electronic structure of TMDs makes them attractive for a variety of applications, as well as electrically active materials in opto-electronics.

...read moreread less

Abstract: Ultrathin two-dimensional nanosheets of layered transition metal dichalcogenides (TMDs) are fundamentally and technologically intriguing. In contrast to the graphene sheet, they are chemically versatile. Mono- or few-layered TMDs - obtained either through exfoliation of bulk materials or bottom-up syntheses - are direct-gap semiconductors whose bandgap energy, as well as carrier type (n- or p-type), varies between compounds depending on their composition, structure and dimensionality. In this Review, we describe how the tunable electronic structure of TMDs makes them attractive for a variety of applications. They have been investigated as chemically active electrocatalysts for hydrogen evolution and hydrosulfurization, as well as electrically active materials in opto-electronics. Their morphologies and properties are also useful for energy storage applications such as electrodes for Li-ion batteries and supercapacitors.

...read moreread less

7,903 citations

1
2
3
4
…
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87
88
89
90
91
92
93
94
95
96
97
98
99
100
101
102
103
104
105
106
107
108
109
110
111
112
113
114
115
116
117
118
119
120
121
122
123
124
125
126
127
128
129
130
131
132
133
134
135
136
137
138
139
140
141
142
143
144
145
146
147
148
149
150
151
152
153
154
155
156
157
158
159
160
161
162
163
164
165
166
167
168
169
170
171
172
173
174
175
176
177
178
179
180
181
182
183
184
185
186
187
188
189
190
191
192
193
194
195
196
197
198
199
200

Collapse

References

PDF

Open Access

More filters

Journal Article•DOI•

Dirac fermion confinement in graphene

[...]

Nuno M. R. Peres¹, A. H. Castro Neto², Francisco Guinea³•Institutions (3)

University of Minho¹, Boston University², Spanish National Research Council³

15 Jun 2006-Physical Review B

TL;DR: In this article, the problem of Dirac fermion confinement in graphene in the presence of a perpendicular magnetic field was studied, and it was shown that confinement leads to anomalies in the electronic spectrum and to a magnetic-field-dependent crossover from Dirac-Landau-level behavior, to linear-in-$B$ behavior, characteristic of confinement.

...read moreread less

Abstract: We study the problem of Dirac fermion confinement in graphene in the presence of a perpendicular magnetic field $B$. We show, analytically and numerically, that confinement leads to anomalies in the electronic spectrum and to a magnetic-field-dependent crossover from $\sqrt{B}$, characteristic of Dirac-Landau-level behavior, to linear-in-$B$ behavior, characteristic of confinement. This crossover occurs when the radius of the Landau level becomes of the order of the width of the system. As a result, we show that the Shubnikov--de Haas oscillations also change as a function of field, and lead to a singular Landau plot.

...read moreread less

142 citations

"The electronic properties of graphe..." refers background or methods in this paper

...Let us now fo us on the opti al ondu tivity, σxx(ω)(Gusynin et al., 2007; Peres et al., 2006 )....
[...]
...(Peres et al., 2006 )....
[...]
...…on line) Energy spe trum (in units of t) for agraphene ribbon 600a wide, as a fun tion of the momentum k along the ribbon (in units of 1/(√3a)), in the presen e of on ning potential with V0 = 1 eV, λ = 180a.Consider the tight-binding des ription (Chen et al.,2007a; Peres et al., 2006b) of Se ....
[...]
...(203)and (204) redu e to: σ0 = 4 π e2 h , (205)whi h is the so- alled universal ondu tivity of graphene(Fradkin, 1986a,b; Katsnelson, 2006b; Lee, 1993;Ludwig et al., 1994; Nersesyan et al., 1994; Peres et al.,2006 ; Tworzydlo et al., 2006; Yang and Nayak, 2002;Ziegler, 1998)....
[...]
...…Dira fermions in a magneti eld (in luding disorder) an be written as: H = H0+Hiwhere H0 is given by (5) and Hi is the impurity potentialreading (Peres et al., 2006 ): Hi = V Ni ∑ j=1 δ(r − rj)I (192)The formulation of the problem in se ond quantizationrequires the solution of H0, whi h was…...
[...]

Journal Article•DOI•

Electron interactions in graphene in a strong magnetic field

[...]

Mark Oliver Goerbig¹, Roderich Moessner², Benoît Douçot¹•Institutions (2)

Centre national de la recherche scientifique¹, École Normale Supérieure²

31 Oct 2006-Physical Review B

TL;DR: The leading symmetry-breaking terms are lattice effects, algebraically small in $a∕{l}_{B}$ as mentioned in this paper, and the leading symmetry breaking terms differ in origin when the Hamiltonian is projected onto the central $(n=0)$ rather than any other Landau levels.

...read moreread less

Abstract: Graphene in the quantum Hall regime exhibits a multicomponent structure due to the electronic spin and chirality degrees of freedom. While the applied field breaks the spin symmetry explicitly, we show that the fate of the chirality SU(2) symmetry is more involved: The leading symmetry-breaking terms differ in origin when the Hamiltonian is projected onto the central $(n=0)$ rather than any other Landau levels. Our description at the lattice level leads to a Harper equation; in its continuum limit, the ratio of lattice constant $a$ and magnetic length ${l}_{B}$ assumes the role of a small control parameter in different guises. The leading symmetry-breaking terms are lattice effects, algebraically small in $a∕{l}_{B}$. We analyze the Haldane pseudopotentials for graphene, and evaluate the easy-plane anisotropy of the graphene ferromagnet.

...read moreread less

141 citations

"The electronic properties of graphe..." refers background in this paper

...…of the di erent broken symmetry phases, in a leansystem, is determined by latti e e e ts, so that it is re-du ed by fa tors of order a/lB, where a is a length ofthe order of the latti e spa ing, and lB is the magneti length (Ali ea and Fisher, 2006, 2007; Goerbig et al.,2006; Wang et al., 2007)....
[...]

Journal Article•DOI•

Electron-electron interactions and the phase diagram of a graphene bilayer

[...]

Johan Nilsson¹, A. H. Castro Neto¹, Nuno M. R. Peres², Francisco Guinea³•Institutions (3)

Boston University¹, University of Minho², Spanish National Research Council³

12 Jun 2006-Physical Review B

TL;DR: In this paper, the effects of long and short-range electron-electron interactions in a graphene bilayer were studied using a variational wave function technique and it was shown that in the presence of long-range Coulomb interactions the clean bilayer is always unstable to electron and hole pocket formation with a finite ferromagnetic polarization.

...read moreread less

Abstract: We study the effects of long and short-range electron-electron interactions in a graphene bilayer. Using a variational wave function technique we show that in the presence of long-range Coulomb interactions the clean bilayer is always unstable to electron and hole pocket formation with a finite ferromagnetic polarization. Furthermore, we argue that short-range electron-electron interactions lead to a staggered orientation of the ordered ferromagnetic moment in each layer (that is, $c$-axis antiferromagnetism). We also comment on the effects of doping and trigonal distortions of the electronic bands.

...read moreread less

141 citations

"The electronic properties of graphe..." refers background in this paper

...The interband ex hangeenergy is redu ed in a bilayer (Nilsson et al., 2006 ), anda positive ontribution that depends logarithmi ally onthe bandwidth in graphene is absent in its bilayer....
[...]
...Furthermore, a ording to Hartree-Fo k al ulations, lean bilayer graphene is unstable towardsferromagnetism (Nilsson et al., 2006b).1....
[...]
...The same result, namely a ondu tan e of the order of e2/h, is obtained for disordered graphene bilayers where aself- onsistent al ulation leads to universal ondu tivityat the neutrality point (Katsnelson, 2007 ; Nilsson et al.,2006a, 2007a)....
[...]
...Higherorder orre tions to (227) lead to a rst order transitionat slightly higher densities (Nilsson et al., 2006 )....
[...]
...Hen e, even in a leansystem, the number of ondu ting hannels in the dire -tion perpendi ular to the layers vanishes at zero energy(Nilsson et al., 2006a, 2007a)....
[...]

Journal Article•DOI•

Edge and surface states in the quantum Hall effect in graphene

[...]

A. H. Castro Neto¹, Francisco Guinea¹, Francisco Guinea², Nuno M. R. Peres³•Institutions (3)

Boston University¹, Spanish National Research Council², University of Minho³

10 May 2006-Physical Review B

TL;DR: In this article, the integer and fractional quantum Hall effect on a honeycomb lattice at half-filling (graphene) in the presence of disorder and electron-electron interactions was studied.

...read moreread less

Abstract: We study the integer and fractional quantum Hall effect on a honeycomb lattice at half-filling (graphene) in the presence of disorder and electron-electron interactions. We show that the interactions between the delocalized chiral edge states (generated by the magnetic field) and Anderson-localized surface states (created by the presence of zig-zag edges) lead to edge reconstruction. As a consequence, the point contact tunneling on a graphene edge has a nonuniversal tunneling exponent, and the Hall conductivity is not perfectly quantized in units of ${e}^{2}∕h$. We argue that the magnetotransport properties of graphene depend strongly on the strength of electron-electron interactions, the amount of disorder, and the details of the edges.

...read moreread less

140 citations

"The electronic properties of graphe..." refers background in this paper

...Fullerenes (C60) aremole ules onsisting of wrapped graphene by the introdu -tion of pentagons on the hexagonal latti e (Castro Neto et al.,2006a).1947) that found it to be a semimetal with unusual lin-early dispersing ele troni ex itations alled Dira ele -trons....
[...]
...When ele tron-hole symmetry is broken(t′ 6= 0) these states be ome dispersive with a Fermi ve-lo ity ve ≈ t′a (Castro Neto et al., 2006b).2....
[...]
...…by the fa t thatin graphene the Dira fermions move with a speed vFwhi h is 300 times smaller than the speed of light, c. Hen e, many of the unusual properties of QED an show up in graphene but at mu h smaller speeds(Castro Neto et al., 2006a; Katsnelson and Novoselov,2007; Katsnelson et al., 2006)....
[...]
...…of edge states(Areshkin and White, 2007; Gunly ke et al., 2007), lead-ing to Anderson lo alization, and anomalies inthe quantum Hall e e t (Castro Neto et al., 2006b;Martin and Blanter, 2007) as well as Coulomb blo k- 17 0 1 2 3 4 5 6 7 -1 0 1 e ne rg y / t 0 0.1 0.2 0.3 0.4 -0.2 0 0.2 0 1 2 3 4…...
[...]
...Edge states in graphene nanoribbons, just as the aseof arbon nanotubes, are predi ted to be Luttinger liq-uids, that is, intera ting one-dimensional ele tron sys-tems (Castro Neto et al., 2006b)....
[...]

Journal Article•DOI•

Four-fermion theory is renormalizable in 2+1 dimensions

[...]

Baruch Rosenstein¹, Brian J. Warr¹, Seon H. Park¹•Institutions (1)

University of Texas at Austin¹

27 Mar 1989-Physical Review Letters

TL;DR: The four-fermion interaction in 2+1 dimensions is nonrenormalizable in weak coupling perturbation theory, but it is shown that this model is in fact renormalizable order by order in the 1/N/sub f/ expansion.

...read moreread less

Abstract: The four-fermion interaction in 2+1 dimensions is nonrenormalizable in weak coupling perturbation theory. We show that this model is in fact renormalizable order by order in the 1/N/sub f/ expansion, and we find this theory a finite ultraviolet fixed point.

...read moreread less

138 citations

"The electronic properties of graphe..." refers background in this paper

...This result re-mains true even to higher order in perturbation theory(Mish henko, 2007) and is also obtained in large N ex-pansions (Rosenstein et al., 1989, 1991; Son, 2007) (N isthe number of avors of Dira fermions), with the onlymodi ation being the prefa tor in (220)....
[...]