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•

Two-Dimensional Porous Carbon: Synthesis and Ion-Transport Properties

[...]

Xiaoyu Zheng¹, Jiayan Luo¹, Wei Lv², Dawei Wang³, Quan-Hong Yang², Quan-Hong Yang¹ - Show less +2 more•Institutions (3)

Tianjin University¹, Tsinghua University², University of New South Wales³

01 Sep 2015-Advanced Materials

TL;DR: Two-dimensional porous carbon sheets with an interlinked hierarchical porous structure are a good candidate for supercapacitors due to their advantages in high aspect ratio for electrode packing and electron transport, hierarchical pore structures for ion transport, and short ion-transport length.

...read moreread less

Abstract: Their chemical stability, high specific surface area, and electric conductivity enable porous carbon materials to be the most commonly used electrode materials for electrochemical capacitors (also known as supercapacitors). To further increase the energy and power density, engineering of the pore structures with a higher electrochemical accessible surface area, faster ion-transport path and a more-robust interface with the electrolyte is widely investigated. Compared with traditional porous carbons, two-dimensional (2D) porous carbon sheets with an interlinked hierarchical porous structure are a good candidate for supercapacitors due to their advantages in high aspect ratio for electrode packing and electron transport, hierarchical pore structures for ion transport, and short ion-transport length. Recent progress on the synthesis of 2D porous carbons is reported here, along with the improved electrochemical behavior due to enhanced ion transport. Challenges for the controlled preparation of 2D porous carbons with desired properties are also discussed; these require precise tuning of the hierarchical structure and a clarification of the formation mechanisms.

...read moreread less

302 citations

Journal Article•DOI•

Direct View of Hot Carrier Dynamics in Graphene

[...]

Jens Christian Johannsen¹, Søren Ulstrup², Federico Cilento, Alberto Crepaldi, Michele Zacchigna³, Cephise Cacho⁴, I. C. Edmond Turcu⁴, Emma Springate⁴, Felix Fromm⁵, Christian Raidel⁵, Thomas Seyller⁵, Fulvio Parmigiani⁶, Marco Grioni¹, Philip Hofmann² - Show less +10 more•Institutions (6)

École Polytechnique Fédérale de Lausanne¹, Aarhus University², AREA Science Park³, Rutherford Appleton Laboratory⁴, Chemnitz University of Technology⁵, University of Trieste⁶

09 Jul 2013-Physical Review Letters

TL;DR: A dynamical view on the Dirac cone is presented by time- and angle-resolved photoemission spectroscopy to show the quasi-instant thermalization of the electron gas to a temperature of ≈2000 K, and to disentangle the subsequent decay into excitations of optical phonons and acoustic phonons.

...read moreread less

Abstract: The ultrafast dynamics of excited carriers in graphene is closely linked to the Dirac spectrum and plays a central role for many electronic and optoelectronic applications. Harvesting energy from excited electron-hole pairs, for instance, is only possible if these pairs can be separated before they lose energy to vibrations, merely heating the lattice. Until now, the hot carrier dynamics in graphene could only be accessed indirectly. Here, we present a dynamical view on the Dirac cone by time-and angle-resolved photoemission spectroscopy. This allows us to show the quasi-instant thermalization of the electron gas to a temperature of approximate to 2000 K, to determine the time-resolved carrier density, and to disentangle the subsequent decay into excitations of optical phonons and acoustic phonons (directly and via supercollisions).

...read moreread less

302 citations

Journal Article•DOI•

Strain Engineering for Phosphorene: The Potential Application as a Photocatalyst

[...]

Baisheng Sa¹, Yan-Ling Li², Jingshan Qi², Rajeev Ahuja³, Rajeev Ahuja⁴, Zhimei Sun⁵ - Show less +2 more•Institutions (5)

Fuzhou University¹, Jiangsu Normal University², Royal Institute of Technology³, Uppsala University⁴, Beihang University⁵

07 Nov 2014-Journal of Physical Chemistry C

TL;DR: In this paper, the authors unraveled strain engineered phosphorene as a photocatalyst in the application of water splitting hydrogen production based on density functional theory calculations and demonstrated the stability for such kind of artificial materials under different strains.

...read moreread less

Abstract: Phosphorene has attracted intense interest due to its unexpected high carrier mobility and distinguished anisotropic optoelectronic and electronic properties. In this work, we unraveled strain engineered phosphorene as a photocatalyst in the application of water splitting hydrogen production based on density functional theory calculations. Lattice dynamic calculations demonstrated the stability for such kind of artificial materials under different strains. The phosphorene lattice is unstable under compression strains and could be crashed, whereas phosphorene lattice shows very good stability under tensile strains. Further guarantee of the stability of phosphorene in liquid water is studied by ab initio molecular dynamics simulations. Tunable band gap from 1.54 eV at ambient condition to 1.82 eV under tensile strains for phosphorene is evaluated using parameter-free hybrid functional calculations. Appropriate band gaps and band edge alignments at certain pH demonstrate the potential application of phosphor...

...read moreread less

302 citations

Journal Article•DOI•

2D V-V Binary Materials: Status and Challenges.

[...]

Shiying Guo¹, Yupeng Zhang², Yanqi Ge², Shengli Zhang¹, Haibo Zeng¹, Han Zhang² - Show less +2 more•Institutions (2)

Nanjing University of Science and Technology¹, Shenzhen University²

01 Sep 2019-Advanced Materials

TL;DR: A review of the historical work is provided for both theoretical predictions and experimental advances of 2D V-V binary materials, and their various intriguing electronic properties are discussed, including band structure, carrier mobility, Rashba effect, and topological state.

...read moreread less

Abstract: 2D phosphorene, arsenene, antimonene, and bismuthene, as a fast-growing family of 2D monoelemental materials, have attracted enormous interest in the scientific community owing to their intriguing structures and extraordinary electronic properties. Tuning the monoelemental crystals into bielemental ones between group-VA elements is able to preserve their advantages of unique structures, modulate their properties, and further expand their multifunctional applications. Herein, a review of the historical work is provided for both theoretical predictions and experimental advances of 2D V-V binary materials. Their various intriguing electronic properties are discussed, including band structure, carrier mobility, Rashba effect, and topological state. An emphasis is also given to their progress in fabricated approaches and potential applications. Finally, a detailed presentation on the opportunities and challenges in the future development of 2D V-V binary materials is given.

...read moreread less

301 citations

Journal Article•DOI•

X-ray photoelectron spectroscopy of graphitic carbon nanomaterials doped with heteroatoms.

[...]

Toma Susi¹, Thomas Pichler¹, Paola Ayala¹•Institutions (1)

University of Vienna¹

15 Jan 2015-Beilstein Journal of Nanotechnology

TL;DR: A practical guide for interpreting X-ray photoelectron spectra of doped graphitic carbon nanomaterials, and a reference for their binding energies that are vital for compositional analysis via XPS are provided.

...read moreread less

Abstract: X-ray photoelectron spectroscopy (XPS) is one of the best tools for studying the chemical modification of surfaces, and in particular the distribution and bonding of heteroatom dopants in carbon nanomaterials such as graphene and carbon nanotubes. Although these materials have superb intrinsic properties, these often need to be modified in a controlled way for specific applications. Towards this aim, the most studied dopants are neighbors to carbon in the periodic table, nitrogen and boron, with phosphorus starting to emerge as an interesting new alternative. Hundreds of studies have used XPS for analyzing the concentration and bonding of dopants in various materials. Although the majority of works has concentrated on nitrogen, important work is still ongoing to identify its precise atomic bonding configurations. In general, care should be taken in the preparation of a suitable sample, consideration of the intrinsic photoemission response of the material in question, and the appropriate spectral analysis. If this is not the case, incorrect conclusions can easily be drawn, especially in the assignment of measured binding energies into specific atomic configurations. Starting from the characteristics of pristine materials, this review provides a practical guide for interpreting X-ray photoelectron spectra of doped graphitic carbon nanomaterials, and a reference for their binding energies that are vital for compositional analysis via XPS.

...read moreread less

299 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•

Electric Field Effect in Atomically Thin Carbon Films

[...]

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.

...read moreread less

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.

...read moreread less

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....
[...]
...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)....
[...]
...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)....
[...]

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.

...read moreread less

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.

...read moreread less

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....
[...]
...…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.,…...
[...]
...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....
[...]

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.

...read moreread less

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

...read moreread less

20,724 citations

Journal Article•DOI•

Two-dimensional gas of massless Dirac fermions in graphene

[...]

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.

...read moreread less

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.

...read moreread less

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....
[...]
...Adapted from(Novoselov et al., 2005a)....
[...]
...Adapted from (Novoselov et al.,2005a).and hen e σxy,inc. = I/VH = ±4Ne2/h, whi h is thenaive expe tation....
[...]
...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 =…...
[...]
...…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)....
[...]