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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Evidence of Topological Surface State in Three-Dimensional Dirac Semimetal Cd3As2

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Hemian Yi¹, Zhijun Wang¹, Chaoyu Chen¹, Youguo Shi¹, Ya Feng¹, Aiji Liang¹, Zhuojin Xie¹, Shaolong He¹, Junfeng He¹, Yingying Peng¹, Xu Liu¹, Yan Liu¹, Lin Zhao¹, Guodong Liu¹, Xiaoli Dong¹, Jun Zhang¹, Masashi Nakatake², Masashi Arita², Kenya Shimada², Hirofumi Namatame², Masaki Taniguchi², Zuyan Xu¹, Chuangtian Chen¹, Xi Dai¹, Zhong Fang¹, Xingjiang Zhou¹ - Show less +22 more•Institutions (2)

Chinese Academy of Sciences¹, Synchrotron Radiation Center²

01 May 2015-Scientific Reports

TL;DR: The electronic structure of Cd3As2 is investigated by angle-resolved photoemission measurements on the crystal surface and detailed band structure calculations and the topological surface state with a linear dispersion approaching the Fermi level is identified for the first time.

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Abstract: The three-dimensional topological semimetals represent a new quantum state of matter. Distinct from the surface state in the topological insulators that exhibits linear dispersion in two-dimensional momentum plane, the three-dimensional semimetals host bulk band dispersions linearly along all directions. In addition to the gapless points in the bulk, the three-dimensional Weyl/Dirac semimetals are also characterized by “topologically protected” surface state with Fermi arcs on their surface. While Cd3As2 is proposed to be a viable candidate of a Dirac semimetal, more investigations are necessary to pin down its nature. In particular, the topological surface state, the hallmark of the three-dimensional semimetal, has not been observed in Cd3As2. Here we report the electronic structure of Cd3As2 investigated by angle-resolved photoemission measurements on the (112) crystal surface and detailed band structure calculations. The measured Fermi surface and band structure show a good agreement with the band structure calculations with two bulk Dirac-like bands approaching the Fermi level and forming Dirac points near the Brillouin zone center. Moreover, the topological surface state with a linear dispersion approaching the Fermi level is identified for the first time. These results provide experimental indications on the nature of topologically non-trivial three-dimensional Dirac cones in Cd3As2.

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169 citations

Journal Article•DOI•

2D layered group IIIA metal chalcogenides: synthesis, properties and applications in electronics and optoelectronics

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Wenjuan Huang¹, Lin Gan¹, Huiqiao Li¹, Ying Ma¹, Tianyou Zhai¹ - Show less +1 more•Institutions (1)

Huazhong University of Science and Technology¹

31 May 2016-CrystEngComm

TL;DR: The remarkable properties of graphene have inspired great research interest in two-dimensional layered materials (2DLMs) with novel electronic and optical attributes as mentioned in this paper, which have shown great potential in electronics and optoelectronics.

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Abstract: The remarkable properties of graphene have inspired great research interest in two-dimensional layered materials (2DLMs) with novel electronic and optical attributes. As a class of graphene-like 2DLMs, ultrathin group IIIA metal chalcogenides (GIIIAMCs, metal = In, Ga; chalcogen = S, Se, Te) have shown great potential in electronics and optoelectronics. In this review, we first introduce the crystal structures and their unique advantages in specific potential applications. Then, we summarize the progress in the fabrication of GIIIAMCs in the framework of top-down and bottom-up methods. Next, their recent achievements regarding enhanced field-effect transistor and photodetector applications are discussed in detail. In addition, the construction strategies of hybrid GIIIAMCs heterostructures and their applications in electronics and optoelectronics are presented. Finally, this review is concluded with some perspectives and an outlook for continued research.

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168 citations

Journal Article•DOI•

CVD growth of fingerprint-like patterned 3D graphene film for an ultrasensitive pressure sensor

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Kailun Xia¹, Chunya Wang¹, Muqiang Jian¹, Qi Wang¹, Yingying Zhang¹ - Show less +1 more•Institutions (1)

Tsinghua University¹

01 Feb 2018-Nano Research

TL;DR: Wang et al. as mentioned in this paper fabricated flexible pressure sensing membranes, which simultaneously showed a high sensitivity of 110 (kPa)−1 for 0-0.2 kPa and wide workable pressure range (up to 75 kPa).

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Abstract: With the rapid development of wearable devices, flexible pressure sensors with high sensitivity and wide workable range are highly desired. In nature, there are many well-adapted structures developed through natural selection, which inspired us for the design of biomimetic materials or devices. Particularly, human fingertip skin, where many epidermal ridges amplify external stimulations, might be a good example to imitate for highly sensitive sensors. In this work, based on unique chemical vapor depositions (CVD)-grown 3D graphene films that mimic the morphology of fingertip skin, we fabricated flexible pressure sensing membranes, which simultaneously showed a high sensitivity of 110 (kPa)−1 for 0–0.2 kPa and wide workable pressure range (up to 75 kPa). Hierarchical structured PDMS films molded from natural leaves were used as the supporting elastic films for the graphene films, which also contribute to the superior performance of the pressure sensors. The pressure sensor showed a low detection limit (0.2 Pa), fast response (< 30 ms), and excellent stability for more than 10,000 loading/unloading cycles. Based on these features, we demonstrated its applications in detecting tiny objects, sound, and human physiological signals, showing its potential in wearable electronics for health monitoring and human/machine interfaces.

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168 citations

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

...Since its discovery in 2004 [44], graphene, as the star of two-dimensional (2D) materials, has gained extensive attention [45, 46]....
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Journal Article•DOI•

A theoretical review on electronic, magnetic and optical properties of silicene.

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Suman Chowdhury¹, Debnarayan Jana¹•Institutions (1)

University of Calcutta¹

18 Oct 2016-Reports on Progress in Physics

TL;DR: The results obtained so far from experimental and theoretical studies in understanding silicene have shown enough significant promising features to open a new direction in the silicon industry, silicon based nano-structures in spintronics and in opto-electronic devices.

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Abstract: Inspired by the success of graphene, various two dimensional (2D) structures in free standing (FS) (hypothetical) form and on different substrates have been proposed recently. Silicene, a silicon counterpart of graphene, is predicted to possess massless Dirac fermions and to exhibit an experimentally accessible quantum spin Hall effect. Since the effective spin-orbit interaction is quite significant compared to graphene, buckling in silicene opens a gap of 1.55 meV at the Dirac point. This band gap can be further tailored by applying in plane stress, an external electric field, chemical functionalization and defects. In this topical theoretical review, we would like to explore the electronic, magnetic and optical properties, including Raman spectroscopy of various important derivatives of monolayer and bilayer silicene (BLS) with different adatoms (doping). The magnetic properties can be tailored by chemical functionalization, such as hydrogenation and introducing vacancy into the pristine planar silicene. Apart from some universal features of optical absorption present in all these 2D materials, the study on reflectivity modulation with doping (Al and P) concentration in silicene has indicated the emergence of some strong peaks having the robust characteristic of a doped reflective surface for both polarizations of the electromagnetic (EM) field. Besides this, attempts will be made to understand the electronic properties of silicene from some simple tight-binding Hamiltonian. We also point out the importance of shape dependence and optical anisotropy properties in silicene nanodisks and establish that a zigzag trigonal possesses the maximum magnetic moment. We also suggest future directions to be explored to make the synthesis of silicene and its various derivatives viable for verification of theoretical predictions. Although this is a fairly new route, the results obtained so far from experimental and theoretical studies in understanding silicene have shown enough significant promising features to open a new direction in the silicon industry, silicon based nano-structures in spintronics and in opto-electronic devices.

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168 citations

Journal Article•DOI•

Controlled synthesis of large-scale, uniform, vertically standing graphene for high-performance field emitters

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Lili Jiang¹, Tianzhong Yang¹, Fei Liu², Jing Dong³, Zhaohui Yao³, Chengmin Shen¹, Shaozhi Deng², Ningsheng Xu², Yunqi Liu¹, Hong-Jun Gao¹ - Show less +6 more•Institutions (3)

Chinese Academy of Sciences¹, Sun Yat-sen University², Tsinghua University³

11 Jan 2013-Advanced Materials

TL;DR: Large-scale, uniform, vertically standing graphene with atomically thin edges are controllably synthesized on copper foil using a microwave-plasma chemical vapor deposition system and shows excellent field-emission properties.

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Abstract: Large-scale, uniform, vertically standing graphene with atomically thin edges are controllably synthesized on copper foil using a microwave-plasma chemical vapor deposition system. A growth mechanism for this system is proposed. This film shows excellent field-emission properties, with low turn-on field of 1.3 V μm(-1) , low threshold field of 3.0 V μm(-1) and a large field-enhancement factor more than 10 000.

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168 citations

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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)....
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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 Article•DOI•

The rise of graphene

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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....
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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•

Theory of elasticity

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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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