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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TL;DR: Topology and collective phenomena give quantum materials emergent functions that provide a platform for developing next-generation quantum technologies, as surveyed in this paper, where the authors present a review of their work.
Abstract: Topology and collective phenomena give quantum materials emergent functions that provide a platform for developing next-generation quantum technologies, as surveyed in this Review.
338 citations
TL;DR: In this article, it was shown that Auger processes play an unusually strong role for the relaxation dynamics of photoexcited charge carriers in graphene, which confirmed the potential of graphene as a new material for high-efficiency photodevices.
Abstract: Graphene as a zero-bandgap semiconductor is an ideal model structure to study the carrier relaxation channels, which are inefficient in conventional semiconductors. In particular, it is of fundamental interest to address the question whether Auger-type processes significantly influence the carrier dynamics in graphene. These scattering channels bridge the valence and conduction band allowing carrier multiplication, a process that generates multiple charge carriers from the absorption of a single photon. This has been suggested in literature for improving the efficiency of solar cells. Here we show, based on microscopic calculations within the density matrix formalism, that Auger processes do play an unusually strong role for the relaxation dynamics of photoexcited charge carriers in graphene. We predict that a considerable carrier multiplication takes place, confirming the potential of graphene as a new material for high-efficiency photodevices.
335 citations
Journal Article•
TL;DR: Theoretical analysis suggests that a chiral superconducting state could emerge in a doped graphene monolayer as discussed by the authors, which is expected to support a variety of exotic and potentially useful phenomena.
Abstract: Chiral superconducting states are expected to support a variety of exotic and potentially useful phenomena. Theoretical analysis suggests that just such a state could emerge in a doped graphene monolayer.
334 citations
Cites background from "The electronic properties of graphe..."
...B 81, 024504 (2010) [7] Castro Neto, A....
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...Here we show that chiral superconductivity with a dx2−y2 ± idxy (d + id) gap structure can be realized in graphene monolayer, a system of choice of modern nanoscience [7, 8]....
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...We note that while the existence of saddle points is a topological property of the FS and is robust to arbitrarily long range hopping, the FS nesting is spoilt by third and higher neighbor hopping effects [7, 12]....
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...At this filling factor, a logarithmic Van Hove singularity originates from three inequivalent saddle points, and the FS also displays a high degree of nesting, forming a perfect hexagon when third and higher neighbor hopping effects are neglected [7, 12] (Fig....
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...b) Conduction band for monolayer graphene [7]....
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TL;DR: In this paper, a transfer matrix method is developed for optical calculations of non-interacting graphene layers, and optical properties such as reflection, transmission and absorption for single-, double-and multi-layer graphene are studied.
Abstract: A transfer matrix method is developed for optical calculations of non-interacting graphene layers. Within the framework of this method, optical properties such as reflection, transmission and absorption for single-, double- and multi-layer graphene are studied. We also apply the method to structures consisting of periodically arranged graphene layers, revealing well-defined photonic band structures and even photonic bandgaps. Finally, we discuss graphene plasmons and introduce a simple way to tune the plasmon dispersion.
331 citations
DOI•
Heidelberg University1, Trinity College, Dublin2, University of Cambridge3, Autonomous University of Madrid4, Université Paris-Saclay5, University of Zaragoza6, Spanish National Research Council7, University of Nottingham8, RWTH Aachen University9, Kessler Foundation10, Istituto Italiano di Tecnologia11, University of Grenoble12, Georgia Institute of Technology13, Dresden University of Technology14, Polytechnic University of Turin15, University of Zurich16, Bielefeld University17, University of Strasbourg18, Technical University of Denmark19, Swiss Federal Laboratories for Materials Science and Technology20, Ikerbasque21, University of Erlangen-Nuremberg22, Technische Universität München23, Bundeswehr University Munich24, University of Bern25, Foundation for Research & Technology – Hellas26, University of Patras27, Center for Theoretical Studies, University of Miami28, École Polytechnique Fédérale de Lausanne29, University of Ulm30, University of Eastern Finland31, Aristotle University of Thessaloniki32, University of Manchester33, Polish Academy of Sciences34, Aalto University35, University of Castilla–La Mancha36, ShanghaiTech University37, University of Exeter38, Chalmers University of Technology39, Warsaw University of Technology40, University of Trieste41, University of Trento42, Instituto Politécnico Nacional43, Queen Mary University of London44, University of the Basque Country45, Chemnitz University of Technology46, Charles University in Prague47, University of Jena48, University of Texas at Dallas49
TL;DR: In this article, the authors present an overview of the main techniques for production and processing of graphene and related materials (GRMs), as well as the key characterization procedures, adopting a 'hands-on' approach, providing practical details and procedures as derived from literature and from the authors' experience, in order to enable the reader to reproduce the results.
Abstract: © 2020 The Author(s). We present an overview of the main techniques for production and processing of graphene and related materials (GRMs), as well as the key characterization procedures. We adopt a 'hands-on' approach, providing practical details and procedures as derived from literature as well as from the authors' experience, in order to enable the reader to reproduce the results. Section I is devoted to 'bottom up' approaches, whereby individual constituents are pieced together into more complex structures. We consider graphene nanoribbons (GNRs) produced either by solution processing or by on-surface synthesis in ultra high vacuum (UHV), as well carbon nanomembranes (CNM). Production of a variety of GNRs with tailored band gaps and edge shapes is now possible. CNMs can be tuned in terms of porosity, crystallinity and electronic behaviour. Section II covers 'top down' techniques. These rely on breaking down of a layered precursor, in the graphene case usually natural crystals like graphite or artificially synthesized materials, such as highly oriented pyrolythic graphite, monolayers or few layers (FL) flakes. The main focus of this section is on various exfoliation techniques in a liquid media, either intercalation or liquid phase exfoliation (LPE). The choice of precursor, exfoliation method, medium as well as the control of parameters such as time or temperature are crucial. A definite choice of parameters and conditions yields a particular material with specific properties that makes it more suitable for a targeted application. We cover protocols for the graphitic precursors to graphene oxide (GO). This is an important material for a range of applications in biomedicine, energy storage, nanocomposites, etc. Hummers' and modified Hummers' methods are used to make GO that subsequently can be reduced to obtain reduced graphene oxide (RGO) with a variety of strategies. GO flakes are also employed to prepare three-dimensional (3d) low density structures, such as sponges, foams, hydro- or aerogels. The assembly of flakes into 3d structures can provide improved mechanical properties. Aerogels with a highly open structure, with interconnected hierarchical pores, can enhance the accessibility to the whole surface area, as relevant for a number of applications, such as energy storage. The main recipes to yield graphite intercalation compounds (GICs) are also discussed. GICs are suitable precursors for covalent functionalization of graphene, but can also be used for the synthesis of uncharged graphene in solution. Degradation of the molecules intercalated in GICs can be triggered by high temperature treatment or microwave irradiation, creating a gas pressure surge in graphite and exfoliation. Electrochemical exfoliation by applying a voltage in an electrolyte to a graphite electrode can be tuned by varying precursors, electrolytes and potential. Graphite electrodes can be either negatively or positively intercalated to obtain GICs that are subsequently exfoliated. We also discuss the materials that can be amenable to exfoliation, by employing a theoretical data-mining approach. The exfoliation of LMs usually results in a heterogeneous dispersion of flakes with different lateral size and thickness. This is a critical bottleneck for applications, and hinders the full exploitation of GRMs produced by solution processing. The establishment of procedures to control the morphological properties of exfoliated GRMs, which also need to be industrially scalable, is one of the key needs. Section III deals with the processing of flakes. (Ultra)centrifugation techniques have thus far been the most investigated to sort GRMs following ultrasonication, shear mixing, ball milling, microfluidization, and wet-jet milling. It allows sorting by size and thickness. Inks formulated from GRM dispersions can be printed using a number of processes, from inkjet to screen printing. Each technique has specific rheological requirements, as well as geometrical constraints. The solvent choice is critical, not only for the GRM stability, but also in terms of optimizing printing on different substrates, such as glass, Si, plastic, paper, etc, all with different surface energies. Chemical modifications of such substrates is also a key step. Sections IV-VII are devoted to the growth of GRMs on various substrates and their processing after growth to place them on the surface of choice for specific applications. The substrate for graphene growth is a key determinant of the nature and quality of the resultant film. The lattice mismatch between graphene and substrate influences the resulting crystallinity. Growth on insulators, such as SiO2, typically results in films with small crystallites, whereas growth on the close-packed surfaces of metals yields highly crystalline films. Section IV outlines the growth of graphene on SiC substrates. This satisfies the requirements for electronic applications, with well-defined graphene-substrate interface, low trapped impurities and no need for transfer. It also allows graphene structures and devices to be measured directly on the growth substrate. The flatness of the substrate results in graphene with minimal strain and ripples on large areas, allowing spectroscopies and surface science to be performed. We also discuss the surface engineering by intercalation of the resulting graphene, its integration with Si-wafers and the production of nanostructures with the desired shape, with no need for patterning. Section V deals with chemical vapour deposition (CVD) onto various transition metals and on insulators. Growth on Ni results in graphitized polycrystalline films. While the thickness of these films can be optimized by controlling the deposition parameters, such as the type of hydrocarbon precursor and temperature, it is difficult to attain single layer graphene (SLG) across large areas, owing to the simultaneous nucleation/growth and solution/precipitation mechanisms. The differing characteristics of polycrystalline Ni films facilitate the growth of graphitic layers at different rates, resulting in regions with differing numbers of graphitic layers. High-quality films can be grown on Cu. Cu is available in a variety of shapes and forms, such as foils, bulks, foams, thin films on other materials and powders, making it attractive for industrial production of large area graphene films. The push to use CVD graphene in applications has also triggered a research line for the direct growth on insulators. The quality of the resulting films is lower than possible to date on metals, but enough, in terms of transmittance and resistivity, for many applications as described in section V. Transfer technologies are the focus of section VI. CVD synthesis of graphene on metals and bottom up molecular approaches require SLG to be transferred to the final target substrates. To have technological impact, the advances in production of high-quality large-area CVD graphene must be commensurate with those on transfer and placement on the final substrates. This is a prerequisite for most applications, such as touch panels, anticorrosion coatings, transparent electrodes and gas sensors etc. New strategies have improved the transferred graphene quality, making CVD graphene a feasible option for CMOS foundries. Methods based on complete etching of the metal substrate in suitable etchants, typically iron chloride, ammonium persulfate, or hydrogen chloride although reliable, are time- and resourceconsuming, with damage to graphene and production of metal and etchant residues. Electrochemical delamination in a low-concentration aqueous solution is an alternative. In this case metallic substrates can be reused. Dry transfer is less detrimental for the SLG quality, enabling a deterministic transfer. There is a large range of layered materials (LMs) beyond graphite. Only few of them have been already exfoliated and fully characterized. Section VII deals with the growth of some of these materials. Amongst them, h-BN, transition metal tri- and di-chalcogenides are of paramount importance. The growth of h-BN is at present considered essential for the development of graphene in (opto) electronic applications, as h-BN is ideal as capping layer or substrate. The interesting optical and electronic properties of TMDs also require the development of scalable methods for their production. Large scale growth using chemical/physical vapour deposition or thermal assisted conversion has been thus far limited to a small set, such as h-BN or some TMDs. Heterostructures could also be directly grown.
330 citations
References
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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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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•
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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
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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