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: The basic properties of graphene plasmons are reviewed: their energy dispersion, localization and propagation, plasmon-phonon hybridization, lifetimes and damping pathways, and emerging and potential applications.
Abstract: In recent years, we have seen a rapid progress in the field of graphene plasmonics, motivated by graphene's unique electrical and optical properties, tunabilty, long-lived collective excitation and their extreme light confinement. Here, we review the basic properties of graphene plasmons; their energy dispersion, localization and propagation, plasmon-phonon hybridization, lifetimes and damping pathways. The application space of graphene plasmonics lies in the technologically significant, but relatively unexploited terahertz to mid-infrared regime. We discuss emerging and potential applications, such as modulators, notch filters, polarizers, mid-infrared photodetectors, mid-infrared vibrational spectroscopy, among many others.
1,056 citations
TL;DR: The guiding principle of the classification is to find irreducible representations of the little group of lattice symmetries at high-symmetry points in the Brillouin zone for each of the 230 space groups (SGs), the dimension of which corresponds to the number of bands that meet at the high-Symmetry point.
Abstract: INTRODUCTION Condensed-matter systems have recently become a fertile ground for the discovery of fermionic particles and phenomena predicted in high-energy physics; examples include Majorana fermions, as well as Dirac and Weyl semimetals. However, fermions in condensed-matter systems are not constrained by Poincare symmetry. Instead, they must only respect the crystal symmetry of one of the 230 space groups. Hence, there is the potential to find and classify free fermionic excitations in solid-state systems that have no high-energy counterparts. RATIONALE The guiding principle of our classification is to find irreducible representations of the little group of lattice symmetries at high-symmetry points in the Brillouin zone (BZ) for each of the 230 space groups (SGs), the dimension of which corresponds to the number of bands that meet at the high-symmetry point. Because we are interested in systems with spin-orbit coupling, we considered only the double-valued representations, where a 2π rotation gives a minus sign. Furthermore, we considered systems with time-reversal symmetry that squares to –1. For each unconventional representation, we computed the low-energy k · p Hamiltonian near the band crossings by writing down all terms allowed by the crystal symmetry. This allows us to further differentiate the band crossings by the degeneracy along lines and planes that emanate from the high-symmetry point, and also to compute topological invariants. For point degeneracies, we computed the monopole charge of the band-crossing; for line nodes, we computed the Berry phase of loops encircling the nodes. RESULTS We found that three space groups exhibit symmetry-protected three-band crossings. In two cases, this results in a threefold degenerate point node, whereas the third case results in a line node away from the high-symmetry point. These crossings are required to have a nonzero Chern number and hence display surface Fermi arcs. However, upon applying a magnetic field, they have an unusual Landau level structure, which distinguishes them from single and double Weyl points. Under the action of spatial symmetries, these fermions transform as spin-1 particles, as a consequence of the interplay between nonsymmorphic space group symmetries and spin. Additionally, we found that six space groups can host sixfold degeneracies. Two of these consist of two threefold degeneracies with opposite chirality, forced to be degenerate by the combination of time reversal and inversion symmetry, and can be described as “sixfold Dirac points.” The other four are distinct. Furthermore, seven space groups can host eightfold degeneracies. In two cases, the eightfold degeneracies are required; all bands come in groups of eight that cross at a particular point in the BZ. These two cases also exhibit fourfold degenerate line nodes, from which other semimetals can be derived: By adding strain or a magnetic field, these line nodes split into Weyl, Dirac, or line node semimetals. For all the three-, six- and eight-band crossings, nonsymmorphic symmetries play a crucial role in protecting the band crossing. Last, we found that seven space groups may host fourfold degenerate “spin-3/2” fermions at high symmetry points. Like their spin-1 counterparts, these quasiparticles host Fermi surfaces with nonzero Chern number. Unlike the other cases we considered, however, these fermions can be stabilized by both symmorphic and nonsymmorphic symmetries. Three space groups that host these excitations also host unconventional fermions at other points in the BZ. We propose nearly 40 candidate materials that realize each type of fermion near the Fermi level, as verified with ab initio calculations. Seventeen of these have been previously synthesized in single-crystal form, whereas others have been reported in powder form. CONCLUSION We have analyzed all types of fermions that can occur in spin-orbit coupled crystals with time-reversal symmetry and explored their topological properties. We found that there are several distinct types of such unconventional excitations, which are differentiated by their degeneracies at and along high-symmetry points, lines, and surfaces. We found natural generalizations of Weyl points: three- and four-band crossings described by a simple k · S Hamiltonian, where S i is the set of spin generators in either the spin-1 or spin-3/2 representations. These points carry a Chern number and, consequently, can exhibit Fermi arc surface states. We also found excitations with six- and eightfold degeneracies. These higher-band crossings create a tunable platform to realize topological semimetals by applying an external magnetic field or strain to the fourfold degenerate line nodes. Last, we propose realizations for each species of fermion in known materials, many of which are known to exist in single-crystal form.
1,054 citations
TL;DR: This work provides a method to fabricate high-quality silicene and an explanation for the formation of the buckled silicenes sheet.
Abstract: Silicene, a two-dimensional (2D) honeycomb structure similar to graphene, has been successfully fabricated on an Ir(111) substrate. It is characterized as a (√7×√7) superstructure with respect to the substrate lattice, as revealed by low energy electron diffraction and scanning tunneling microscopy. Such a superstructure coincides with the (√3×√3) superlattice of silicene. First-principles calculations confirm that this is a (√3×√3)silicene/(√7×√7)Ir(111) configuration and that it has a buckled conformation. Importantly, the calculated electron localization function shows that the silicon adlayer on the Ir(111) substrate has 2D continuity. This work provides a method to fabricate high-quality silicene and an explanation for the formation of the buckled silicene sheet.
1,044 citations
TL;DR: In this article, the authors studied the phonon-limited mobility in intrinsic $n$-type single-layer MoS for temperatures $Tg100$ K. The mobility is weakly dependent on the carrier density.
Abstract: We study the phonon-limited mobility in intrinsic $n$-type single-layer MoS${}_{2}$ for temperatures $Tg100$ K. The materials properties including the electron-phonon interaction are calculated from first principles and the deformation potentials and Fr\"ohlich interaction in single-layer MoS${}_{2}$ are established. The calculated room-temperature mobility of $\ensuremath{\sim}$410 cm${}^{2}$V${}^{\ensuremath{-}1}$s${}^{\ensuremath{-}1}$ is found to be dominated by optical phonon scattering via intra and intervalley deformation potential couplings and the Fr\"ohlich interaction. The mobility is weakly dependent on the carrier density and follows a $\ensuremath{\mu}\ensuremath{\sim}{T}^{\ensuremath{-}\ensuremath{\gamma}}$ temperature dependence with $\ensuremath{\gamma}=1.69$ at room temperature. It is shown that a quenching of the characteristic homopolar mode, which is likely to occur in top-gated samples, increases the mobility with $\ensuremath{\sim}$70 cm${}^{2}$V${}^{\ensuremath{-}1}$s${}^{\ensuremath{-}1}$ and can be observed as a decrease in the exponent to $\ensuremath{\gamma}=1.52$. In comparison to recent experimental findings for the mobility in single-layer MoS${}_{2}$ ($\ensuremath{\sim}$200 cm${}^{2}$V${}^{\ensuremath{-}1}$s${}^{\ensuremath{-}1}$), our results indicate that mobilities close to the intrinsic phonon-limited mobility can be achieved in two-dimensional materials via dielectric engineering that effectively screens static Coulomb scattering on, e.g., charged impurities.
1,036 citations
TL;DR: In this article, a perspective on the experimental efforts toward the development of microwave absorbers composed of carbonaceous inclusions in a polymer matrix is presented. But the authors focus on the application for which the absorber is intended, weight reduction and optimization of the operating bandwidth are two important issues.
Abstract: Carbon (C) is a crucial material for many branches of modern technology. A growing number of demanding applications in electronics and telecommunications rely on the unique properties of C allotropes. The need for microwave absorbers and radar-absorbing materials is ever growing in military applications (reduction of radar signature of aircraft, ships, tanks, and targets) as well as in civilian applications (reduction of electromagnetic interference among components and circuits, reduction of the back-radiation of microstrip radiators). Whatever the application for which the absorber is intended, weight reduction and optimization of the operating bandwidth are two important issues. A composite absorber that uses carbonaceous particles in combination with a polymer matrix offers a large flexibility for design and properties control, as the composite can be tuned and optimized via changes in both the carbonaceous inclusions (C black, C nanotube, C fiber, graphene) and the embedding matrix (rubber, thermoplastic). This paper offers a perspective on the experimental efforts toward the development of microwave absorbers composed of carbonaceous inclusions in a polymer matrix. The absorption properties of such composites can be tailored through changes in geometry, composition, morphology, and volume fraction of the filler particles. Polymercomposites filled with carbonaceous particles provide a versatile system to probe physical properties at the nanoscale of fundamental interest and of relevance to a wide range of potential applications that span radar absorption, electromagnetic protection from natural phenomena (lightning), shielding for particle accelerators in nuclear physics, nuclear electromagnetic pulse protection, electromagnetic compatibility for electronic devices, high-intensity radiated field protection, anechoic chambers, and human exposure mitigation. Carbonaceous particles are also relevant to future applications that require environmentally benign and mechanically flexible materials.
1,026 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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