Showing papers in "Physical Review B in 2010"

Electronic Structure of Pyrochlore Iridates: From Topological Dirac Metal to Mott Insulator

Abstract: In 5d transition metal oxides such as the iridates, novel properties arise from the interplay of electron correlations and spin-orbit interactions. We investigate the electronic structure of the pyrochlore iridates, (such as Y$_{2}$Ir$_{2}$O$_{7}$) using density functional theory, LDA+U method, and effective low energy models. A remarkably rich phase diagram emerges on tuning the correlation strength U. The Ir magnetic moment are always found to be non-collinearly ordered. However, the ground state changes from a magnetic metal at weak U, to a Mott insulator at large U. Most interestingly, the intermediate U regime is found to be a Dirac semi-metal, with vanishing density of states at the Fermi energy. It also exhibits topological properties - manifested by special surface states in the form of Fermi arcs, that connect the bulk Dirac points. This Dirac phase, a three dimensional analog of graphene, is proposed as the ground state of Y$_{2}$Ir$_{2}$O$_{7}$ and related compounds. A narrow window of magnetic `axion' insulator, with axion parameter $\theta=\pi$, may also be present at intermediate U. An applied magnetic field induces ferromagnetic order and a metallic ground state.

Higher-accuracy van der Waals density functional

Abstract: We propose a second version of the van der Waals density functional of Dion et al. [Phys. Rev. Lett. 92, 246401 (2004)], employing a more accurate semilocal exchange functional and the use of a large-N asymptote gradient correction in determining the vdW kernel. The predicted binding energy, equilibrium separation, and potential-energy curve shape are close to those of accurate quantum chemical calculations on 22 duplexes. We anticipate the enabling of chemically accurate calculations in sparse materials of importance for condensed matter, surface, chemical, and biological physics.

Crystal structure prediction via particle-swarm optimization

Abstract: We have developed a method for crystal structure prediction from ``scratch'' through particle-swarm optimization (PSO) algorithm within the evolutionary scheme. PSO technique is different with the genetic algorithm and has apparently avoided the use of evolution operators (e.g., crossover and mutation). The approach is based on an efficient global minimization of free-energy surfaces merging total-energy calculations via PSO technique and requires only chemical compositions for a given compound to predict stable or metastable structures at given external conditions (e.g., pressure). A particularly devised geometrical structure parameter which allows the elimination of similar structures during structure evolution was implemented to enhance the structure search efficiency. The application of designed variable unit-cell size technique has greatly reduced the computational cost. Moreover, the symmetry constraint imposed in the structure generation enables the realization of diverse structures, leads to significantly reduced search space and optimization variables, and thus fastens the global structure convergence. The PSO algorithm has been successfully applied to the prediction of many known systems (e.g., elemental, binary, and ternary compounds) with various chemical-bonding environments (e.g., metallic, ionic, and covalent bonding). The high success rate demonstrates the reliability of this methodology and illustrates the promise of PSO as a major technique on crystal structure determination.

Recombination in polymer-fullerene bulk heterojunction solar cells

Abstract: Recombination of photogenerated charge carriers in polymer bulk heterojunction (BHJ) solar cells reduces the short circuit current $({J}_{sc})$ and the fill factor (FF). Identifying the mechanism of recombination is, therefore, fundamentally important for increasing the power conversion efficiency. Light intensity and temperature-dependent current-voltage measurements on polymer BHJ cells made from a variety of different semiconducting polymers and fullerenes show that the recombination kinetics are voltage dependent and evolve from first-order recombination at short circuit to bimolecular recombination at open circuit as a result of increasing the voltage-dependent charge carrier density in the cell. The ``missing 0.3 V'' inferred from comparison of the band gaps of the bulk heterojunction materials and the measured open-circuit voltage at room-temperature results from the temperature dependence of the quasi-Fermi levels in the polymer and fullerene domains---a conclusion based on the fundamental statistics of fermions.

Many-body localization phase transition

Abstract: We use exact diagonalization to explore the many-body localization transition in a random-field spin-1/2 chain. We examine the correlations within each many-body eigenstate, looking at all high-energy states and thus effectively working at infinite temperature. For weak random field the eigenstates are thermal, as expected in this nonlocalized, ``ergodic'' phase. For strong random field the eigenstates are localized with only short-range entanglement. We roughly locate the localization transition and examine some of its finite-size scaling, finding that this quantum phase transition at nonzero temperature might be showing infinite-randomness scaling with a dynamic critical exponent $z\ensuremath{\rightarrow}\ensuremath{\infty}$.

Topological characterization of periodically driven quantum systems

Abstract: Topological properties of physical systems can lead to robust behaviors that are insensitive to microscopic details. Such topologically robust phenomena are not limited to static systems but can also appear in driven quantum systems. In this paper, we show that the Floquet operators of periodically driven systems can be divided into topologically distinct (homotopy) classes and give a simple physical interpretation of this classification in terms of the spectra of Floquet operators. Using this picture, we provide an intuitive understanding of the well-known phenomenon of quantized adiabatic pumping. Systems whose Floquet operators belong to the trivial class simulate the dynamics generated by time-independent Hamiltonians, which can be topologically classified according to the schemes developed for static systems. We demonstrate these principles through an example of a periodically driven two-dimensional hexagonal lattice tight-binding model which exhibits several topological phases. Remarkably, one of these phases supports chiral edge modes even though the bulk is topologically trivial.

Superconductivity in the iron selenide K x Fe 2 Se 2 (0≤x≤1.0)

Abstract: We report the superconductivity at above 30 K in a FeSe-layer compound K0.8Fe2Se2 (nominal composition) achieved by metal K intercalating in between FeSe layers. It is isostructural to BaFe2As2 and possesses the highest T-c for FeSe-layer materials so far under ambient pressure. Hall effect indicates the carriers are dominated by electron in this superconductor. We confirm that the observed superconductivity at above 30 K is due to this FeSe-based 122 phase. Our results demonstrate that FeSe-layer materials are really remarkable superconductors via structure and carrier modulation.

Optimized Tersoff and Brenner empirical potential parameters for lattice dynamics and phonon thermal transport in carbon nanotubes and graphene

Abstract: We have examined the commonly used Tersoff and Brenner empirical interatomic potentials in the context of the phonon dispersions in graphene. We have found a parameter set for each empirical potential that provides improved fits to some structural data and to the in-plane phonon-dispersion data for graphite. These optimized parameter sets yield values of the acoustic-phonon velocities that are in better agreement with measured data. They also provide lattice thermal conductivity values in single-walled carbon nanotubes and graphene that are considerably improved compared to those obtained from the original parameter sets.

Majorana fermions in a tunable semiconductor device

Abstract: The experimental realization of Majorana fermions presents an important problem due to their non-Abelian nature and potential exploitation for topological quantum computation. Very recently Sau et al. [Phys. Rev. Lett. 104, 040502 (2010)] demonstrated that a topological superconducting phase supporting Majorana fermions can be realized using surprisingly conventional building blocks: a semiconductor quantum well coupled to an s-wave superconductor and a ferromagnetic insulator. Here we propose an alternative setup, wherein a topological superconducting phase is driven by applying an in-plane magnetic field to a (110)-grown semiconductor coupled only to an s-wave superconductor. This device offers a number of advantages, notably a simpler architecture and the ability to tune across a quantum phase transition into the topological superconducting state while still largely avoiding unwanted orbital effects. Experimental feasibility of both setups is discussed in some detail.

Entanglement spectrum of a topological phase in one dimension

Abstract: We show that the Haldane phase of $S=1$ chains is characterized by a double degeneracy of the entanglement spectrum. The degeneracy is protected by a set of symmetries (either the dihedral group of $\ensuremath{\pi}$ rotations about two orthogonal axes, time-reversal symmetry, or bond centered inversion symmetry), and cannot be lifted unless either a phase boundary to another, ``topologically trivial,'' phase is crossed, or the symmetry is broken. More generally, these results offer a scheme to classify gapped phases of one-dimensional systems. Physically, the degeneracy of the entanglement spectrum can be observed by adiabatically weakening a bond to zero, which leaves the two disconnected halves of the system in a finitely entangled state.

Relating the open-circuit voltage to interface molecular properties of donor:acceptor bulk heterojunction solar cells

Abstract: The open-circuit voltage (V-oc) of polymer:fullerene bulk heterojunction solar cells is determined by the interfacial charge-transfer (CT) states between polymer and fullerene. Fourier-transform ph ...

Optical response features of Si-nanoparticle arrays

Abstract: Periodic structures of spherical silicon particles are analyzed using the coupled-dipole equations for studying optical response features and local electromagnetic fields. The model takes into account the electric and magnetic dipole moments of the particles embedded in a homogeneous dielectric medium. Particles with radius of 65 nm and larger are considered. It is shown that, due to the large permittivity of silicon, the first two Mie resonances are located in the region of visible light, where the absorption is small and the extinction is basically determined by scattering. The main contribution is given by the induced magnetic and electric dipoles of the particles. Thus, in contrast to metal particle arrays, here is a possibility to combine separately either the electric or magnetic dipole resonances of individual particles with the structural features. As a result, extinction spectra can have additional narrow resonant peaks connected with multiple light scattering by the magnetic dipoles and displaying a Fano-type resonant profile. Reflection and transmission properties of the Si particle arrays are investigated and the conditions of low light reflection and transmission by the particle arrays are discussed, as well as the applicability of the dipole approach. It is shown that the light transmission of finite-size arrays of Si particles can be significantly suppressed at the conditions of the particle magnetic dipole resonance. It is demonstrated that, using resonant conditions, one can separately control the enhancements of local electric and magnetic fields in the structures.

Flat bands in slightly twisted bilayer graphene: tight-binding calculations

Abstract: The presence of flat bands near Fermi level has been proposed as an explanation for high transition temperature superconductors. The bands of graphite are extremely sensitive to topological defects which modify the electronic structure. In this Rapid Communication, we found nondispersive flat bands no farther than 10 meV of the Fermi energy in slightly twisted bilayer graphene as a signature of a transition from a parabolic dispersion of bilayer graphene to the characteristic linear dispersion of graphene. This transition occurs for relative rotation angles of layers around $1.5\ifmmode^\circ\else\textdegree\fi{}$ and is related to a process of layer decoupling. We have performed ab initio calculations to develop a tight-binding model with an interaction Hamiltonian between layers that include the $\ensuremath{\pi}$ orbitals of all atoms and takes into account interactions up to third nearest neighbors within a layer.

Local unitary transformation, long-range quantum entanglement, wave function renormalization, and topological order

Abstract: Two gapped quantum ground states in the same phase are connected by an adiabatic evolution which gives rise to a local unitary transformation that maps between the states. On the other hand, gapped ground states remain within the same phase under local unitary transformations. Therefore, local unitary transformations define an equivalence relation and the equivalence classes are the universality classes that define the different phases for gapped quantum systems. Since local unitary transformations can remove local entanglement, the above equivalence/universality classes correspond to pattern of long-range entanglement, which is the essence of topological order. The local unitary transformation also allows us to define a wave function renormalization scheme, under which a wave function can flow to a simpler one within the same equivalence/universality class. Using such a setup, we find conditions on the possible fixed-point wave functions where the local unitary transformations have finite dimensions. The solutions of the conditions allow us to classify this type of topological orders, which generalize the string-net classification of topological orders. We also describe an algorithm of wave function renormalization induced by local unitary transformations. The algorithm allows us to calculate the flow of tensor-product wave functions which are not at the fixed points. This will allow us to calculate topological orders as well as symmetry-breaking orders in a generic tensor-product state.

Flexural phonons and thermal transport in graphene

Abstract: We show through an exact numerical solution of the phonon Boltzmann equation that the lattice thermal conductivity of graphene is dominated by contributions from the out-of-plane or flexural phonon modes, previously thought to be negligible. We connect this unexpected result to the anomalously large density of states of flexural phonons compared to their in-plane counterparts and to a symmetry-based selection rule that significantly restricts anharmonic phonon-phonon scattering of the flexural modes. The result is found to hold in the presence of the ripples known to occur in graphene, phonon-isotopic impurity scattering, and rigidity of the flexural phonon branch arising from the long-wavelength coupling between flexural and in-plane modes. Finally, accurate inclusion of the momentum conserving Normal phonon-phonon scattering processes within the context of a full solution of the phonon Boltzmann equation are shown to be essential in accurately describing the graphene thermal conductivity, in contrast to the more commonly used relaxation time and long wavelength approximations.

Model Hamiltonian for topological insulators

Abstract: In this paper we give the full microscopic derivation of the model Hamiltonian for the three-dimensional topological insulators in the ${\mathrm{Bi}}_{2}{\mathrm{Se}}_{3}$ family of materials (${\mathrm{Bi}}_{2}{\mathrm{Se}}_{3}$, ${\mathrm{Bi}}_{2}{\mathrm{Te}}_{3}$ and ${\mathrm{Sb}}_{2}{\mathrm{Te}}_{3}$). We first give a physical picture to understand the electronic structure by analyzing atomic orbitals and applying symmetry principles. Subsequently, we give the full microscopic derivation of the model Hamiltonian introduced by Zhang et al. [Nat. Phys. 5, 438 (2009)] based both on symmetry principles and the $\mathbf{k}\ensuremath{\cdot}\mathbf{p}$ perturbation theory. Two different types of ${k}^{3}$ terms, which break the in-plane full rotation symmetry down to threefold rotation symmetry, are taken into account. An effective Hamiltonian is derived for the topological surface states. Both bulk and surface models are investigated in the presence of an external magnetic field, and the associated Landau level structure is presented. For a more quantitative fitting to the first principle calculations, we also present a model Hamiltonian including eight energy bands.

Evolution of the Raman spectra from single-, few-, and many-layer graphene with increasing disorder

Abstract: We report on the micro-Raman spectroscopy of monolayer, bilayer, trilayer, and many layers of graphene (graphite) bombarded by low-energy argon ions with different doses. The evolution of peak frequencies, intensities, linewidths, and areas of the main Raman bands of graphene is analyzed as function of the distance between defects and number of layers. We describe the disorder-induced frequency shifts and the increase in the linewidth of the Raman bands by means of a spatial-correlation model. Also, the evolution of the relative areas ${A}_{D}/{A}_{G}$, ${A}_{{D}^{\ensuremath{'}}}/{A}_{G}$, and ${A}_{{G}^{\ensuremath{'}}}/{A}_{G}$ is described by a phenomenological model. The present results can be used to fully characterize disorder in graphene systems.

Topological Defects and Gapless Modes in Insulators and Superconductors

Abstract: We develop a unified framework to classify topological defects in insulators and superconductors described by spatially modulated Bloch and Bogoliubov de Gennes Hamiltonians. We consider Hamiltonians $\mathcal{H}(\mathbf{k},\mathbf{r})$ that vary slowly with adiabatic parameters $\mathbf{r}$ surrounding the defect and belong to any of the ten symmetry classes defined by time-reversal symmetry and particle-hole symmetry. The topological classes for such defects are identified and explicit formulas for the topological invariants are presented. We introduce a generalization of the bulk-boundary correspondence that relates the topological classes to defect Hamiltonians to the presence of protected gapless modes at the defect. Many examples of line and point defects in three-dimensional systems will be discussed. These can host one dimensional chiral Dirac fermions, helical Dirac fermions, chiral Majorana fermions, and helical Majorana fermions, as well as zero-dimensional chiral and Majorana zero modes. This approach can also be used to classify temporal pumping cycles, such as the Thouless charge pump, as well as a fermion parity pump, which is related to the Ising non-Abelian statistics of defects that support Majorana zero modes.

Topological defects in graphene: Dislocations and grain boundaries

Abstract: Topological defects in graphene, dislocations and grain boundaries, are still not well understood despite the considerable number of experimental observations. We introduce a general approach for constructing dislocations in graphene characterized by arbitrary Burgers vectors as well as grain boundaries, covering the whole range of possible misorientation angles. By using ab initio calculations we investigate thermodynamic and electronic properties of these topological defects, finding energetically favorable symmetric large-angle grain boundaries, strong tendency toward out-of-plane deformation in the small-angle regimes, and pronounced effects on the electronic structure. The present results show that dislocations and grain boundaries are important intrinsic defects in graphene which may be used for engineering graphene-based nanomaterials and functional devices.

Large bulk resistivity and surface quantum oscillations in the topological insulator Bi 2 Te 2 Se

Abstract: Topological insulators are predicted to present interesting surface transport phenomena but their experimental studies have been hindered by a metallic bulk conduction that overwhelms the surface transport. We show that the topological insulator ${\text{Bi}}_{2}{\text{Te}}_{2}\text{Se}$ presents a high resistivity exceeding $1\text{ }\ensuremath{\Omega}\text{ }\text{cm}$ and a variable-range hopping behavior, and yet presents Shubnikov-de Haas oscillations coming from the topological surface state. Furthermore, we have been able to clarify both the bulk and surface transport channels, establishing a comprehensive understanding of the transport in this material. Our results demonstrate that ${\text{Bi}}_{2}{\text{Te}}_{2}\text{Se}$ is, to our knowledge, the best material to date for studying the surface quantum transport in a topological insulator.

Intrinsic point defects and complexes in the quaternary kesterite semiconductor Cu(2)ZnSnS(4)

Abstract: Current knowledge of the intrinsic defect properties of ${\text{Cu}}_{2}{\text{ZnSnS}}_{4}$ (CZTS) is limited, which is hindering further improvement of the performance of CZTS-based solar cells. Here, we have performed first-principles calculations for a series of intrinsic defects and defect complexes in CZTS, from which we have the following observations. (i) It is important to control the elemental chemical potentials during crystal growth to avoid the formation of secondary phases such as ZnS, CuS, and ${\text{Cu}}_{2}{\text{SnS}}_{3}$. (ii) The intrinsic $p$-type conductivity is attributed to the ${\text{Cu}}_{\text{Zn}}$ antisite which has a lower formation energy and relatively deeper acceptor level compared to the Cu vacancy. (iii) The low formation energy of many of the acceptor defects will lead to the intrinsic $p$-type character, i.e., $n$-type doping is very difficult in this system. (iv) The role of electrically neutral defect complexes is predicted to be important, because they have remarkably low formation energies and electronically passivate deep levels in the band gap. For example, $[{\text{Cu}}_{\text{Zn}}^{\ensuremath{-}}+{\text{Zn}}_{\text{Cu}}^{+}]$, $[{V}_{\text{Cu}}^{\ensuremath{-}}+{\text{Zn}}_{\text{Cu}}^{+}]$, and $[{\text{Zn}}_{\text{Sn}}^{2\ensuremath{-}}+2{\text{Zn}}_{\text{Cu}}^{+}]$ may form easily in nonstoichiometric samples. The band alignment between ${\text{Cu}}_{2}{\text{ZnSnS}}_{4}$, ${\text{CuInSe}}_{2}$ and the solar-cell window layer CdS has also been calculated, revealing that a type-II band alignment exists for the $\text{CdS}/{\text{Cu}}_{2}{\text{ZnSnS}}_{4}$ heterojunction. The fundamental differences between CZTS and ${\text{CuInSe}}_{2}$ for use in thin-film photovoltaics are discussed. The results are expected to be relevant to other ${\text{I}}_{2}{\text{-II-IV-VI}}_{4}$ semiconductors.

Skyrmion lattice in the doped semiconductor Fe1-xCoxSi

Abstract: We report a comprehensive small angle neutron scattering study of the magnetic phase diagram of the doped semiconductor ${\text{Fe}}_{1\ensuremath{-}x}{\text{Co}}_{x}\text{Si}$ for $x=0.2$. For magnetic field parallel to the neutron beam we observe a sixfold intensity pattern under field cooling. The regime of the skyrmion lattice is highly hysteretic and extents over a wide temperature range as may be expected due to the site disorder of the Fe and Co atoms. Our study identifies ${\text{Fe}}_{1\ensuremath{-}x}{\text{Co}}_{x}\text{Si}$ as the second material in which a skyrmion lattice forms and establishes that skyrmion lattices exist also in doped semiconductors.

Theory of magnon-driven spin Seebeck effect

Abstract: The spin Seebeck effect is a spin-motive force generated by a temperature gradient in a ferromagnet that can be detected via normal metal contacts through the inverse spin Hall effect [K. Uchida et al., Nature (London) 455, 778 (2008)]. We explain this effect by spin pumping at the contact that is proportional to the spin-mixing conductance of the interface, the inverse of a temperature-dependent magnetic coherence volume, and the difference between the magnon temperature in the ferromagnet and the electron temperature in the normal metal [D. J. Sanders and D. Walton, Phys. Rev. B 15, 1489 (1977)].

Effects of strain on electronic properties of graphene

Abstract: We present first-principles calculations of electronic properties of graphene under uniaxial and isotropic strains, respectively. The semimetallic nature is shown to persist up to a very large uniaxial strain of 30% except a very narrow strain range where a tiny energy gap opens. As the uniaxial strain increases along a certain direction, the Fermi velocity parallel to it decreases quickly and vanishes eventually, whereas the Fermi velocity perpendicular to it increases by as much as 25%. Thus, the low energy properties with small uniaxial strains can be described by the generalized Weyl's equation while massless and massive electrons coexist with large ones. The work function is also predicted to increase substantially as both the uniaxial and isotropic strain increases. Hence, the homogeneous strain in graphene can be regarded as the effective electronic scalar potential.

Spectroscopic ellipsometry of graphene and an exciton-shifted van Hove peak in absorption

Abstract: We demonstrate that optical transparency of any two-dimensional system with a symmetric electronic spectrum is governed by the fine structure constant and suggest a simple formula that relates a quasiparticle spectrum to an optical absorption of such a system. These results are applied to graphene deposited on a surface of oxidized silicon for which we measure ellipsometric spectra, extract optical constants of a graphene layer and reconstruct the electronic dispersion relation near the K point using optical transmission spectra. We also present spectroscopic ellipsometry analysis of graphene placed on amorphous quartz substrates and report a pronounced peak in ultraviolet absorption at 4.6 eV because of a van Hove singularity in graphene's density of states. The peak is asymmetric and downshifted by 0.5 eV probably due to excitonic effects.

Quantum anomalous Hall effect in graphene from Rashba and exchange effects

Abstract: We investigate the possibility of realizing quantum anomalous Hall effect in graphene. We show that a bulk energy gap can be opened in the presence of both Rashba spin-orbit coupling and an exchange field. We calculate the Berry curvature distribution and find a nonzero Chern number for the valence bands and demonstrate the existence of gapless edge states. Inspired by this finding, we also study, by first-principles method, a concrete example of graphene with Fe atoms adsorbed on top, obtaining the same result.

Hybrid functional studies of the oxygen vacancy in TiO 2

Abstract: The electronic and structural properties of the oxygen vacancy $({V}_{\text{O}})$ in rutile ${\text{TiO}}_{2}$ are studied using generalized Kohn-Sham theory with the Heyd, Scuseria, and Ernzerhof (HSE) hybrid functional for exchange and correlation. The HSE approach corrects the band gap and allows for a proper description of defects with energy levels close to the conduction band. According to the HSE calculations, ${V}_{\text{O}}$ is a shallow donor for which the $+2$ charge state is lower in energy than the neutral and $+1$ charge states for all Fermi-level positions in the band gap. The formation energy of ${V}_{\text{O}}^{2+}$ is relatively low in $n$-type ${\text{TiO}}_{2}$ under O-poor conditions but it rapidly increases with the oxygen chemical potential. This is consistent with experimental observations where the electrical conductivity decreases with oxygen partial pressure.

Antiferromagnetic topological insulators

Abstract: We consider antiferromagnets breaking both time-reversal $(\ensuremath{\Theta})$ and a primitive-lattice translational symmetry $({T}_{1/2})$ of a crystal but preserving the combination $S=\ensuremath{\Theta}{T}_{1/2}$. The $S$ symmetry leads to a ${\mathbb{Z}}_{2}$ topological classification of insulators, separating the ordinary insulator phase from the ``antiferromagnetic topological insulator'' phase. This state is similar to the ``strong'' topological insulator with time-reversal symmetry and shares with it such properties as a quantized magnetoelectric effect. However, for certain surfaces the surface states are intrinsically gapped with a half-quantum Hall effect $[{\ensuremath{\sigma}}_{xy}={e}^{2}/(2h)]$, which may aid experimental confirmation of $\ensuremath{\theta}=\ensuremath{\pi}$ quantized magnetoelectric coupling. Step edges on such a surface support gapless, chiral quantum wires. In closing we discuss GdBiPt as a possible example of this topological class.

Massive Dirac fermions and spin physics in an ultrathin film of topological insulator

Abstract: We study transport and optical properties of the surface states, which lie in the bulk energy gap of a thin-film topological insulator. When the film thickness is comparable with the surface-state decay length into the bulk, the tunneling between the top and bottom surfaces opens an energy gap and form two degenerate massive Dirac hyperbolas. Spin-dependent physics emerges in the surface bands, which are vastly different from the bulk behavior. These include the surface spin Hall effects, spin-dependent orbital magnetic moment, and spin-dependent optical transition selection rule, which allows optical spin injection. We show a topological quantum phase transition where the Chern number of the surface bands changes when varying the thickness of the thin film.

Drude conductivity of Dirac fermions in graphene

Abstract: Electrons moving in graphene behave as massless Dirac fermions, and they exhibit fascinating low-frequency electrical transport phenomena. Their dynamic response, however, is little known at frequencies above one terahertz (THz). Such knowledge is important not only for a deeper understanding of the Dirac electron quantum transport, but also for graphene applications in ultrahigh-speed THz electronics and infrared (IR) optoelectronics. In this paper, we report measurements of high-frequency conductivity of graphene from THz to mid-IR at different carrier concentrations. The conductivity exhibits Drude-like frequency dependence and increases dramatically at THz frequencies, but its absolute strength is lower than theoretical predictions. This anomalous reduction of free-electron oscillator strength is corroborated by corresponding changes in graphene interband transitions, as required by the sum rule.