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We investigate the dynamic optical transition of monolayer silicene in the presence of external electric and exchange fields within the low-energy tight-binding model. Applying external electric and exchange fields breaks the silicene band structure spin and valley degeneracies. Three phases of silicene corresponding to different strengths of perpendicular electric field with respect to the spin–orbit coupling (Δ z < Δso, Δ z = Δso and Δ z > Δso) are considered. We obtain the spin-valley-dependent optical responses to the incoming circularly polarized light using the Kubo formula. We show and discuss how the magnitude and direction of the transverse and longitudinal optical responses of such a system change with the electric and exchange fields. Our calculations suggest that the intraband part of the longitudinal optical response as well as the initial point of the interband part have strong dependencies on the exchange field. Furthermore, we show that one of the spin subbands plays a dominant role in the response to polarized light. Depending on the type of incident light polarization, the dominant subband may change. Our results shed light on the relation between silicene dynamic optical responses and externally applied fields.

In this work, we study the band structures and intrinsic anomalous Hall conductivity (AHC) of the ferromagnetic multiorbital tight-binding (TB) model derived from the transition metal compound Sr$_2$RuO$_4$ under periodic driving of monochromatic polarized light. Within the framework of the Floquet theory, we adopt the continued fraction technique to attain the effective Hamiltonian valid in the weak-driving and low-frequency regimes, and the related Green's functions which are further employed for the transport calculations based on the Kubo formalism. The high-frequency circularly and linearly polarized (LP) light has limited impacts on the band structures, while the low-frequency light with the photon energy smaller than the bandwidth of the system opens up bandgaps at the edges of the Floquet-Brillouin zone (FBZ) since the transitions between Floquet sidebands become significant. For intrinsic AHC, the left-handed circularly polarized (LCP) light plays a distinct role on AHC compared to the right-handed circularly polarized (RCP) light. Furthermore, it reveals that the roles of LCP and RCP light can be interchanged by altering the incident plane of light. Finally, the intrinsic AHC with the interplay between the short-range disorder and circularly polarized light is also investigated.

We present a derivation of the full formula to calculate the Berry curvature on non-orthogonal numerical atomic orbital (NAO) bases. Because usually, the number of NAOs is larger than that of the Wannier bases, we use a orbital contraction method to reduce the basis sizes, which can greatly improve the calculation efficiency without significantly reducing the calculation accuracy. We benchmark the formula by calculating the Berry curvature of ferroelectric BaTiO3and bcc Fe, as well as the anomalous Hall conductivity for Fe. The results are in excellent agreement with the finite-difference and previous results in the literature. We find that there are corrections terms to the Kubo formula of the Berry curvature. For the full NAO base, the differences between the two methods are negligibly small, but for the reduced bases sets, the correction terms become larger, which may not be neglected in some cases. The formula developed in this work can readily be applied to the non-orthogonal generalized Wannier functions.

We show that the resistivity in each phase of the high-Tc cuprates is a special case of a general expression derived from the Kubo formula. We obtain, in particular, the T-linear behavior in the strange metal and upper pseudogap phases, the pure T 2 Fermi liquid behavior observed in the strongly overdoped regime as well as in the mid-pseudogap phase. We also describe the T 1 + δ behavior that interpolates the linear and quadratic behaviors in the crossover regime. We calculate the coefficients: (a) of T in the linear regime and show that it is proportional to the pseudogap transition temperature T *(x); (b) of the T 2-term in the Fermi Liquid regime, without adjusting any parameter; and (c) of the T 1.6 term in the crossover regime, all in excellent agreement with the experimental data. From our model, we are able to infer that the resistivity in cuprates is caused by the scattering of holes by excitons, which naturally form as holes are doped into the electron background.

Strain effects have been widely addressed in monolayer black phosphorus (MBP) due to its significant influence on the orbital hybridization of atoms. In this theoretical contribution, we use the tight-binding model, the Harrison rule and the Kubo formula to describe the optical refraction and absorption of MBP in detail. The analytical study of the band gap in strained MBP demonstrates electronic phase transitions from semiconductor-to-semimetal/metal and semiconductor-to-insulator, in which both the compressive and tensile strains act linearly on the band gap alterations. The critical strains corresponding to these phase transitions are fully characterized as well. Our calculations show that the variation of the refraction inflections and absorption peaks depends on the strained band gap, however; the band gap changes under out-of-plane strains are different than the in-plane ones. The conditions under which this discrepancy is significant and/or negligible are investigated. Moreover, the dedication of minimal/maximal optical refraction and/or absorption in MBP to both in-plane and out-of-plane strains are fully addressed. Our theoretical results clarify the strain-induced interplay between the band gap and optical properties to propose a wide range of applications in nano-optoelectronics.

Within the theoretical framework of Kubo formula and self-consistent Born approximation, we theoretically study the transversal and longitudinal magneto-conductivity of a type-I Weyl semimetal. We focus mainly on the peculiar role of inter-valley scattering on linear transversal magnetoresistance (LTMR) and negative longitudinal magnetoresistance (NLMR). At first, we find that the contributions of high-order Feynman diagrams to the transversal magneto-conductivity play the distinct roles between the cases of intra- and inter-valley scatterings. The former suppresses the transversal conductivity whereas the latter enhances it. Then, with the increase of scattering strength, the LTMR is destroyed, accompanying a sizable increase of transversal conductivity, in particular, in the case of the tilted cone. For longitudinal magneto-transport, inter-valley scattering contributes only trivial magnetoresistance. In contrast, intra-valley scattering is invalid for longitudinal magneto-transport which means a very large NLMR. In addition, the high-order Feynman diagrams always play the nontrivial role on the longitudinal conductivity even in the weak scattering limit. Finally, when altering the Fermi energy among low-lying Landau level, the peaks of transversal conductivity just correspond to the valleys of the longitudinal conductivity.

Twisted bilayer graphene is a chiral system which has been recently shown to present circular dichroism. In this work we show that the origin of this optical activity is the rotation of the Dirac fermions’ helicities in the top and bottom layer. Starting from the Kubo formula, we obtain a compact expression for the Hall conductivity that takes into account the dephasing of the electromagnetic field between the top and bottom layers and gathers all the symmetries of the system. Our results are based in both a continuum and a tight-binding model, and they can be generalized to any two-dimensional Dirac material with a chiral stacking between layers., ESM acknowledges financial support by Chilean FONDECYT grant 11130129. LC and LB acknowledge financial support by the Spanish MINECO Grant No. FIS2015–64654-P.

In this paper, the ratio of shear viscosity to entropy density in the context of dRGT massive gravity is studied. The massive graviton breaks the diffeomorphism invariance in the bulk geometry so that the momentum dissipates in the boundary theory. The ratio is calculated numerically and analytically by using Kubo formula. It is shown that exhibits a non-trivial temperature dependence. We find that approaches to a constant value at high temperature, while it tends to zero with a scaling law at low temperature.

The magnetoresistance (MR) in semimetals with Dirac (or Weyl) electrons and free holes is investigated on the basis of the Boltzmann theory. The MR is modified from the conventional results with free electrons and holes in a very complex way due to the correction of the Dirac dispersion. The obtained formula explicitly includes the magnetic field dependence, which is very useful for the analysis of experimental results. In order to verify the validity of our results, the results obtained by the Boltzmann approach are compared with those by the Kubo theory. It is revealed that, by taking into account the field dependence of carrier density, the MR obtained by the Boltzmann theory almost perfectly agrees with that based on the Kubo theory even in the high-field region (in the quantum limit) except for the quantum oscillations. It is also shown that the MR in semimetals increases linearly with respect to the field in the quantum limit due to the drastic change of the carrier density, which is a significant characteristic of semimetals.

Within the framework of finite temperature feld theory this paper discusses the shear viscosity of hot QED plasma through Kubo formula at one-loop skeleton diagram level with a finite chemical potential. The effective widths (damping rates) are introduced to regulate the pinch singularities and then gives a reliable estimation of the shear viscous coefficient. The finite chemical potential contributes positively compared to the pure temperature case. The result agrees with that from the kinetics theory qualitatively.

We consider the movement of a particle advected by a random flow of the form $\vv+\delta \bF(\vx)$, with $\vv\in\R^d$ a constant drift, $\bF(\vx)$ -- the fluctuation -- given by a zero mean, stationary random field and $\delta\ll 1$ so that the drift dominates over the fluctuation. The two-point correlation matrix $\bR(\vx)$ of the random field decays as $|\vx|^{2\alpha-2}$, as $|\vx|\to+\infty$ with $\alpha

The dc conductivity at T = 0 K of half-metallic diluted antiferromagnetic semiconductors and their super lattice is calculated by the use of the Kubo–Greenwood formula applied to the Korringa–Kohn–Rostoker (KKR) Green's function method and the coherent potential approximation in the framework of the local density approximation (LDA) of the density functional method (KKR-CPA-LDA). The calculated dc conductivity of superstructures composed of diluted antiferromagnetic semiconductors shows significant dependence on the magnetic structure of the superstructures. The mechanisms responsible for such behaviour are discussed on the basis of the first-principles calculation.

An exact real-space renormalization method is developed to address the electronic transport in mirror Fibonacci chains at a macroscopic scale by means of the Kubo-Greenwood formula. The results show that the mirror symmetry induces a large number of transparent states in the dc conductivity spectra, contrary to the simple Fibonacci case. A length scaling analysis over ten orders of magnitude reveals the existence of critically localized states and their ac conduction spectra show a highly oscillating behaviour. For multidimensional quasiperiodic systems, a novel renormalization plus convolution method is proposed. This combined renormalization + convolution method has shown an extremely elevated computing efficiency, being able to calculate electrical conductance of a three-dimensional non-crystalline solid with 10 30 atoms. Finally, the dc and ac conductances of mirror Fibonacci nanowires are also investigated, where a quantized dc-conductance variation with the Fermi energy is found, as observed in gold nanowires.

We present the generalization to the binary Yukawa mixture of equilibrium molecular dynamic computations of the transport coefficients of the Yukawa one-component plasma (Salin and Caillol 2002 Phys. Rev. Lett. 88 065002, Salin and Caillol 2000 J. Chem. Phys. 113 10459–63). The simulations were performed within periodic boundary conditions, and Ewald sums were implemented for the potentials, the forces and for all the currents which enter the Kubo formulae. Results include shear and bulk viscosities, ionic thermal conductivity, as in the one-component case, but also diffusion and interdiffusion coefficients. We will present the different coefficients and examples of simulations. We shall also compare our simulation results for large screening parameters with Chapman–Enskog theory (Chapman and Cowling 1970 The Mathematical Theory of Non-Uniform Gases 3rd edn (Cambridge: Cambridge University Press)).

During an adiabatic pumping cycle a conventional two barrier quantum device takes an electron from the left lead and ejects it to the right lead. Hence the pumped charge per cycle is naively expected to be $Q \le e$. This zero order adiabatic point of view is in fact misleading. For a closed device we can get ${Q > e}$ and even ${Q \gg e}$. In this paper a detailed analysis of the quantum pump operation is presented. Using the Kubo formula for the geometric conductance, and applying the Dirac chains picture, we derive practical estimates for~$Q$., 19 pages, 8 figs, minor textual corretions, to be published in JPA

We study the quantum analog of stirring of water inside a cup using a spoon. This can be regarded as a prototype example for quantum pumping in closed devices. The current in the device is induced by translating a scatterer. Its calculation is done using the Kubo formula approach. The transported charge is expressed as a line integral that encircles chains of Dirac monopoles. For simple systems the results turn out to be counter intuitive: e.g. as we move a small scatterer "forward" the current is induced "backwards". One should realize that the route towards quantum-classical correspondence has to do with "quantum chaos" considerations, and hence assumes greater complexity of the device. We also point out the relation to the familiar $S$ matrix formalism which is used to analyze quantum pumping in open geometries., Comment: 20 pages, 12 figures, improved Introduction

An approach to computing conductances of tunnel junctions within the framework of the Landauer-Buttiker theory for electronic transport is introduced and formulated for the Korringa-Kohn-Rostoker (KKR) method for electronic-structure calculations. After a general introduction to the idea behind the approach, tests and comparisons with other methods, namely a 'transmission of Bloch-waves' approach and an approach based on the Kubo-Greenwood formula for the conductivity tensor, reveal a high accuracy and robustness of the proposed method, thus proving its suitability for state-of-the-art computations of spin-dependent ballistic transport. Based on Green functions, it is flexible and can easily be implemented in present KKR computer codes.

In this paper we present a novel approach combining linear response theory (Kubo) for the conductance and the Density Matrix Renormalization Group (DMRG). The system considered is one-dimensional and consists of non-interacting tight binding leads coupled to an interacting nanostructure via weak links. Electrons are treated as spinless fermions and two different correlation functions are used to evaluate the conductance. Exact diagonalization calculations in the non-interacting limit serve as a benchmark for our combined Kubo and DMRG approach in this limit. Including both weak and strong interaction we present DMRG results for an extended nanostructure consisting of seven sites. For the strongly interacting structure a simple explanation of the position of the resonances is given in terms of hard-core particles moving freely on a lattice of reduced size., 7 pages, 2 figures. Minor typos corrected

We report results of first-principles calculations on the thermodynamic stability of different Sr adatom structures that have been proposed to explain some of the observed reconstructions of the (001) surface of strontium titanate (Kubo and Nozoye 2003 Surf. Sci. 542 177). From surface free energy calculations, a phase diagram is constructed indicating the range of conditions over which each structure is most stable. These results are compared with Kubo and Nozoye's experimental observations. It is concluded that low Sr adatom coverage structures can only be explained if the surface is far from equilibrium. Intermediate coverage structures are stable only if the surface is in or very nearly in equilibrium with the strontium oxide.

Based on the Kubo formula for an electron tunneling junction, we revisit the nonequilibrium transport properties through a quantum dot. Since the Fermi level of the quantum dot is set by the conduction electrons of the leads, we calculate the electron current from the left side by assuming the quantum dot coupled to the right lead as another side of the tunneling junction, and the other way round is used to calculate the current from the right side. By symmetrizing these two currents, an effective local density states on the dot can be obtained, and is discussed at high and low temperatures, respectively.

The electronic structure and residual resistivity of diluted (Ga, Mn)As magnetic semiconductors are calculated from first principles using the linear muffin-tin orbital method, the coherent potential approximation, and the Kubo-Greenwood linear response theory. Particular attention is paid to the role of native compensating defects such as As antisites and Mn interstitials as well as to different magnetic configurations of the local Mn moments. The order of magnitude of the calculated resistivities compares reasonably well with available experimental data. The concentration variations of the resistivity reflect two basic mechanisms, namely the strength of the impurity scattering and the number of carriers. In agreement with a recent experiment, the calculated resistivities are strongly correlated with the alloy Curie temperatures evaluated in terms of a classical Heisenberg Hamiltonian.

The optical properties of Co/Cu multilayers are investigated theoretically using a multiband tight-binding model and the results are compared to experimental data on the magneto-refractive effect (MRE). The optical conductivity of both parallel and antiparallel configurations of Co/Cu multilayers is calculated using the Kubo–Greenwood formula. The Kramers–Kronig relations are utilized to obtain the imaginary part of the conductivity and the real part of the dielectric function. The conductivity is decomposed into the intraband and interband terms, so that their different contributions to the MRE may be analysed. In particular, we find that the competition between the intraband and interband contributions leads to a change of sign in the MRE as a function of frequency, a feature which is also observed experimentally in the infrared region. This is in contrast to the predictions of the Drude model, where only the intraband part of the conductivity is considered and the MRE curve always takes the same sign. Therefore, it is vital to include the interband contribution for a full spectral study of the origin of the infrared MRE data.

Extraordinary Hall effect (EHE) in bilayer F/S(N) was investigated theoretically. The conductivity tensor $\sigma_{\alpha\beta}$ is calculated in the Kubo formalism with Green functions found as the solutions of the Gorkov equations. We considered diffuse transport in the ferromagnetic layer, taking into account as a main mechanism of electron resistivity s-d scattering. In this model Gorkov equations for s-electrons in the ferromagnetic layer remain linear and are solved easily. It is shown that Hall field $E^H$ for both F/S and F/N contacts are step-functions of the coordinate perpendicular to the planes of the layers and have zero value in S(N) layer. The Andreev reflection increases the value of Hall constant $R_s$ for F/S case. The value of the Hall constant is $R_H^{F/S} = R_H^{bulk} (\sigma^{\uparrow} + \sigma^{\downarrow})^2 / 4 \sigma^{\uparrow}\sigma^{\downarrow}$, where $\sigma^{\uparrow}$ and $\sigma^{\downarrow}$ are conductivities of electrons with up and down spins, and $R_H^{bulk}$ is the Hall constant in the bulk ferromagnetic metal. In fact, $R_H^{F/S}$ coincides with EHE constant of the bilayer of two ferromagnetic metals with equal thickness and opposite directions of their magnetizations. So we can make a conclusion, that the ideal interface between ferromagnetic metal and superconductor may be considered like a mirror with inversion in spin space.

Rigorous theory of the tunnelling magnetoresistance (TMR) based on the real-space Kubo formula and fully realistic tight-binding bands fitted to an ab initio band structure is described. It is first applied to calculate the TMR of two Co electrodes separated by a vacuum gap. The calculated TMR ratio reaches ≈65% in the tunnelling regime but can be as high as 280% in the metallic regime when the vacuum gap is of the order of the Co interatomic distance (abrupt domain wall). It is also shown that the spin polarization P of the tunnelling current is negative in the metallic regime but becomes positive P≈35% in the tunnelling regime. Calculation of the TMR of an epitaxial Fe/MgO/Fe(001) junction is also described. The calculated optimistic TMR ratio is in excess of 1000% for an MgO barrier of ≈20 atomic planes and the spin polarization of the tunnelling current is positive for all MgO thicknesses. It is also found that spin-dependent tunnelling in an Fe/MgO/Fe(001) junction is not entirely determined by states at the Γ point (k∥ = 0) even for MgO thicknesses as large as ≈20 atomic planes. Finally, it is demonstrated that the TMR ratio calculated from the Kubo formula remains non-zero when one of the Co electrodes is covered with a copper layer. It is shown that non-zero TMR is due to quantum well states in the Cu layer which do not participate in transport. Since these only occur in the down-spin channel, their loss from transport creates a spin asymmetry of electrons tunnelling from a Cu interlayer, i.e. non-zero TMR. Numerical modelling is used to show that diffuse scattering from a random distribution of impurities in the barrier may cause quantum well states to evolve into propagating states, in which case the spin asymmetry of the non-magnetic layer is lost and with it the TMR.

The electrical resistivity of disordered, partially ordered and long-range–ordered gold-copper alloys was calculated from first principles by applying the coherent-potential approximation (CPA) and the Kubo-Greenwood equation to lattices with 2 or 4 atoms per unit cell and varying the occupation probabilities within each cell. In a first step the composition-dependent resistivity for disordered alloys and alloys with the highest possible degree of order was calculated for the entire composition range. After this the experimental resistivity as a function of composition was modelled by calculating the resistivity based on reasonable values for the concentration-dependent order parameter and using lattice structures determined from the phase diagram for each concentration. The experimental resistivity for annealed alloys with its pronounced minima for the two stoichiometric compositions could be perfectly reproduced.

We study the low temperature thermal conductivity of single-layer transition metal dichalcogenides. In the low temperature regime where heat is carried primarily through transport of electrons, thermal conductivity is linked to electrical conductivity through the Wiedemann-Franz law. Using a \textit{k.p} Hamiltonian that describes the $ K $ and $ K^{'} $ valley edges, we compute the zero-frequency electric (Drude) conductivity using the Kubo formula to obtain a numerical estimate for the thermal conductivity. The impurity scattering determined transit time of electrons which enters the Drude expression is evaluated within the self-consistent Born approximation. The analytic expressions derived show that low temperature thermal conductivity 1) is determined by the band gap at the valley edges in monolayer TMDCs and 2) in presence of disorder which can give rise to the variable range hopping regime, there is a distinct reduction. Additionally, we compute the Mott thermopower and demonstrate that under a high frequency light beam that sets up a Floquet Hamiltonian, a valley-resolved thermopower can be obtained. A closing summary reviews the implications of results followed by a brief discussion on applicability of the Wiedemann-Franz law and its breakdown in context of the presented calculations., 9 pages, 6 figures

A topological insulator (TI) thin film differs from the more typically studied thick TI system in that the former has both a top and a bottom surface where the states localized at both surfaces can couple to one other across the finite thickness. An out-of-plane magnetic field leads to the formation of discrete Landau level states in the system, whereas an in-plane magnetization breaks the angular momentum symmetry of the system. In this work, we study the spin accumulation induced by the application of an in-plane electric field to the TI thin film system where the Landau level states and inter-surface coupling are simultaneously present. We show, via Kubo formula calculations, that the in-plane spin accumulation perpendicular to the magnetization due to the electric field vanishes for a TI thin film with symmetric top and bottom surfaces. A finite in-plane spin accumulation perpendicular to both the electric field and magnetization emerges upon applying either a differential magnetization coupling or a potential difference between the two film surfaces. This spin accumulation results from the breaking of the antisymmetry of the spin accumulation around the k-space equal-energy contours.

We formulate a fully self-consistent, microscopic model to study the retardation and correlation effects of the barrier within a Josephson junction. The junction is described by a series of planes, with electronic correlation included through a local self energy for each plane. We calculate current-phase relationships for various junctions, which include non-magnetic impurities in the barrier region, or an interfacial scattering potential. Our results indicate that the linear response of the supercurrent to phase across the barrier region is a good, but not exact indicator of the critical current. Our calculations of the local density of states show the current-carrying Andreev bound states and their energy evolution with the phase difference across the junction. We calculate the figure of merit for a Josephson junction, which is the product of the critical current, Ic, and the normal state resistance, R(N), for junctions with different barrier materials. The normal state resistance is calculated using the Kubo formula, for a system with zero current flow and no superconducting order. Semiclassical calculations would predict that these two quantities are determined by the transmission probabilities of electrons in such a way that the product is constant for a given superconductor at fixed temperature. Our self-consistent solutions for different types of barrier indicate that this is not the case. We suggest some forms of barrier which could increase the Ic.R(N) product, and hence improve the frequency response of a Josephson device., 46 pages, 21 figures

A calculation of the optical conductivity and related optical properties of liquid silicon is presented. Starting from the results of a single superchain/effective medium approximation for the electronic properties, the frequency dependent conductivity is evaluated in terms of the Kubo-Greenwood formula. For a fast computation of the three and four centre terms therein the effective handling of the angular dependences of the Green's functions known from the sp³-fluid model is generalized to the current matrix elements. A good agreement of our results with experimental data for liquid silicon is found. At higher frequencies (>5 eV) and in the fitted Drude parameters, however, there are discrepancies due to the limitations of the sp³-model.

Theoretical studies of the conductance of ferromagnetic and paramagnetic nanowires are performed within the framework of a three-dimensional s-d model. The attention is focused on spin-dependent conductance quantization, which manifests itself in a spectacular way when a circuit becomes open and the conduction goes down in discrete steps. A new approach is developed by assuming that in the last stages of the breaking of the nanocontact, there are fewer and fewer conduction paths, distributed at random and stretching across the contact region. Conductances are calculated within the quasiballistic regime, using the Kubo formula and a recursion Green's function technique. The results for weak ferromagnets (both majority and minority d bands intersect the Fermi surface) are qualitatively different from those for strong ferromagnets (only the minority d bands do), which may explain why experimental cumulative histograms of the conductance reveal more pronounced peaks in the case of Fe than for Ni, and consequently the latter are more sensitive to surface contaminations (oxidization).

The double exchange (DE) model with quantum local spins S is studied; an equation of motion approach is used and decoupling approximations analogous to Hubbard's are made. Our approximate one-electron Green function G is exact in the atomic limit of zero bandwidth for all S and band filling n, and as n->0 reduces to a dynamical coherent potential approximation (CPA) due to Kubo; we regard our approximation as a many-body generalisation of Kubo's CPA. G is calculated self-consistently for general S in the paramagnetic state and for S=1/2 in a state of arbitrary magnetization. The electronic structure is investigated and four bands per spin are obtained centred on the atomic limit peaks of the spectral function. A resistivity formula appropriate to the model is derived from the Kubo formula and the paramagnetic state resistivity rho is calculated; insulating states are correctly obtained at n=0 and n=1 for strong Hund coupling. Our prediction for rho is much too small to be consistent with experiments on manganites so we agree with Millis et al that the bare DE model is inadequate. We show that the agreement with experiment obtained by Furukawa is due to his use of an unphysical density of states., 20 pages, 8 figures, submitted to J. Phys.: Condens. Matter

A microscopic model for the description of the proton subsystem dynamics in superionic crystals with hydrogen bonds is developed. Besides the inclusion of the proton-transport mechanism, the effect of the displacement of the nearest oxygens during hydrogen-bond formation is taken into account. The latter effect is the cause of the strong proton-phonon coupling that leads to the polaronic effect. Using the occupation number formalism, the virtual (in superionic phases) or ordered (in low-temperature phases) character of the hydrogen-bonded system is taken into account on the basis of the proton-ordering model. Protonic conductivity studies are carried out in the framework of the Kubo theory for the cases of superionic phases as well as low-temperature phases with different types of proton ordering (as an example the M3H(XO4)2 class of crystals is considered). The temperature dependencies of the conductivity are analysed. The activation energies for the static conductivity are determined; for this case the influence of the internal field which appears as a result of the proton ordering is investigated.

By a very accurate recursion method based on the Kubo formula we calculate tunneling conductances of systems consisting of a nonmagnetic metallic spacer (MS) sandwiched between two ferromagnets (F) with additional ultra-thin nonmetallic (NM) interface layers. These hybrid structures are attached to voltage contacts by semi-infinite ideal lead wires (LW). The problem is treated in a two-band tight-binding model with hybridization. Our main finding is that the low-resistivity spin electron channel depends on the energy barrier width of the nonmetallic layer, and that with an asymmetric placement of the NM interface layers one can get large positive or negative values of the giant magnetoresistance with current-perpendicular-to-plane.

The high-frequency magnetoconductivity for a double-layer electron - hole system is calculated at finite temperature. The formalism rests on the temperature Green's function and Kubo's formula for conductivity. It is found that at frequencies higher than the cyclotron frequencies of electrons and holes, the frequency-dependent electromagnetic absorption exhibits oscillatory behaviour. The maxima in the absorption coefficient correspond to a situation where the photon energy is approximately the sum of the energies of the electron pair and the hole pair which are simultaneously excited by the radiation field.

The self-diffusion coefficients of the two ionic species in the melt are evaluated using the Green - Kubo formulae. The evaluation is based on a simple model wherein the dynamics of a two-component system is made use of, which relates the self-diffusion coefficients to the pair potential and partial structure factor of the melt through frequency sum rules of the velocity auto-correlation function. Results thus obtained convincingly explain the increase in difference between the two diffusion coefficients with increasing x as observed in a molecular dynamics study. This difference is explicitly related to the different structural back-scattering of ions influenced by their screening due to the presence of valence electrons.

We demonstrate that the giant magnetoresistance (GMR) effect in magnetic multilayers can be explained quantitatively in terms of the scattering of electrons from a spin- independent random potential that arises from the grown-in defects within the multilayer. We have calculated the GMR ratio for Co/Cu and Fe/Cr multilayered systems within the Kubo- Greenwood formalism assuming that the on-site atomic energies are disordered randomly within a realistic spd tight-binding model. Our predictions are in good agreement with experiment and demonstrate how the GMR ratio depends on the features of the electronic band structure. In particular, we obtain the enhancement of GMR in Co/Cu multilayers at electron energies up to about 1 eV above the Fermi level that has recently been observed by Monsma et al (1995 Phys. Rev. Lett. 74 5260). We predict no such enhancement for Fe/Cr multilayers. The mechanism of giant magnetoresistance (GMR) in magnetic multilayers (1) is usually related to the spin dependence of the scattering processes. In the semiclassical models of GMR this spin dependence is introduced into the theory through a number of spin-dependent phenomenological parameters such as relaxation times and transmission coefficients (2, 3). In the quantum mechanical models the spin dependence of the scattering is assumed to arise from spin-dependent random potentials produced by magnetic impurities at the interfaces or in the bulk of the ferromagnetic layers (4-6). These models usually take the electronic structure of the host material to be spin independent, assuming that transport is carried out by the s electrons which are described by the free-electron model (2-5) or by the single- band tight-binding model (6). Recently, however, it has been shown that in the ballistic regime of conductance the spin dependence of the electronic structure already gives a sizeable contribution to GMR (7). Several attempts have been made at combining this realistic description of the electronic structure with spin-dependent scattering potentials for a predictive model of the diffusive regime (8-10). Unfortunately, these calculations imply unrealistically large values of the GMR compared to experiment. In this letter we demonstrate that a realistic prediction of GMR can be obtained within a model that introduces spin-independent disorder in the on-site atomic energy levels in conjunction with accurate spin-dependent electronic structure. In particular, we will show that this model predicts the recently observed enhancement of GMR for hot electrons in Co/Cu spin valves (11). Our model is motivated by experimental observations that magnetic multilayers contain a lot of defects such as vacancies, impurities and grain boundaries that are produced during the process of deposition (e.g. (12)). Each of these defects makes its own contribution to the scattering potential and, consequently, to the resistivity. However, on average there is no reason for this random scattering potential to be spin dependent. One would expect the appearance of a strong spin dependence only for the case when chemically

Using the well-known Kubo formula, we evaluate magnetotransport quantities like the collisional and Hall conductivities of the $\alpha$-T$_3$ model. The collisional conductivity exhibits a series of peaks at strong magnetic field. Each of the conductivity peaks for $\alpha=0$ (graphene) splits into two in presence of a finite $\alpha$. This splitting occurs due to a finite phase difference between the contributions coming from the two valleys. The density of states is also calculated to explore the origin of the splitting of conductivity peaks. As $\alpha$ approaches $1$, the right split part of the conductivity peak comes closer to the left split part of the next conductivity peak. At $\alpha=1$, they merge with each other to produce a new series of the conductivity peaks. On the other hand, the Hall conductivity undergoes a smooth transition from $\sigma_{yx}=2(2n+1)e^2/h$ to $\sigma_{yx}=4ne^2/h$ with $n=0,1,2,...$ as we tune $\alpha$ from $0$ to $1$. For intermediate $\alpha$, we obtain the Hall plateaus at values $0,2,4,6,8,...$ in units of $e^2/h$., Comment: To appear in Journal of Physics: Condensed Matter

We use an extended quasiclassical approach to calculate the two-point conductivity tensor in magnetic multilayers. The obtained result is shown to be identical to that derived from the Kubo formula, indicating a close connection between the Boltzmann and Kubo approaches.

In a recent experiment Weiss et al. (Phys. Rev. Lett., 70 (1993) 4118) observed novel quantum oscillations in the magnetoconductance of large antidot lattices whose classical dynamics is chaotic. Using a semiclassical approach to the Kubo formula, we derive analytical expressions for quantum corrections to the conductivity in terms of the classical periodic orbits of the system which explain the observations by Weiss et al. The contribution from each periodic orbit oscillates as a function of magnetic field and Fermi energy with the phase given by the classical action. The amplitude is determined by the stability of the orbit and disorder-dependent velocity correlations. We also show that these quantum oscillations are related to Shubnikov-de Haas oscillations.

The frequency-dependent conductivity (resistivity) of two isolated parallel electron layers is calculated. The authors take into account both the direct electron-electron interaction and the coupling between electrons through phonon exchange. It is found that the interlayer momentum relaxation due to the direct Coulomb interaction and the phonon exchange interaction has the same dependence on the layer separation. The results for the conductivity rests on the Kubo formula for conductivity and the Green function formalism. The numerical results for the temperature dependence of sigma 12 in the DC limit is presented. Furthermore, they have calculated the frequency dependence of sigma 12 in the zero-temperature limit.

On the basis of the two-zone hybrid model of doped semiconductors and the Kubo formula, the authors have calculated electrical conductivity of Si:P for various impurity concentrations and temperatures. As a basis for conductivity calculations, one-particle Green functions calculated by the modified Matsubara-Toyozawa method are used. Results obtained are compared with the experimental values. Although the agreement is not yet quite satisfactory, significant improvement is evident in comparison with results obtained by other authors using similar methods.

The author presents a method for obtaining the conductance within the linear response approximation of a disordered system of finite cross section described by a tight-binding Hamiltonian. This method is an extension of previous work in which he proposed a numerical algorithm for evaluating the Kubo formula in the spirit of the recursion method. He obtains simple recursive equations for the conductance that can be easily computed. As an application the problem of ballistic transport through a constriction is studied using a confining model potential that allows one to investigate the dependence of the conductance quantisation as a function of Fermi energy, gate voltage and channel length. It is found that the conductance steps as a function of gate voltage are sensitive to the channel length. The possible extension of this work for use in studying the AC transport in these systems is briefly discussed.

This work covers an ab initio calculation of transport and optical properties of plastics of the effective composition CH2 at density 0.954 g/cm3 in the temperature range from 5 kK up to 100 kK. The calculation is based on the quantum molecular dynamics, density functional theory and the Kubo-Greenwood formula. The temperature dependence of the static electrical conductivity σ1DC (T) has an unusual shape: σ1DC(T) grows rapidly for 5 kK ≤ T ≤ 10 kK and is almost constant for 20 kK ≤ T ≤ 60 kK. The additional analysis based on the investigation of the electron density of states (DOS) was performed. The rapid growth of σ1DC(T) at 5 kK ≤ T ≤ 10 kK is connected with the increase of DOS at the electron energy equal to the chemical potential ɛ = μ. The frequency dependence of the dynamic electrical conductivity σ1(ω) at 5 kK has the distinct non-Drude shape with the peak at ω ≈ 10 eV. This behavior of σ1(ω) was explained by the dip at the electron DOS.

The calculation of the gluon plasma viscosity has been performed by lattice simulations in the SU(2) gluodynamics at T/Tc = 1.2 on the supercomputers. The evaluation is based on the Kubo formula that relates viscosity to the spectral function of the correlation functions of the energy-momentum tensor. For the extraction of the spectral function from the Euclidean correlator the linear method is applied.

The magnetoconductivity of bismuth is theoretically investigated on the basis of the Kubo formula to interpret the longstanding mystery of linear magnetoresistance in bismuth. First, the magnetoconductivity for the isotropic Dirac model is studied. It is found that the inverse magnetoconductivity increases quadratically at low magnetic fields and is saturated at high fields. This high field property is in contrast to that obtained by the semiclassical theory, where the inverse magnetoconductivity keeps quadratic increase. Next, the magnetoconductivity for the extended Dirac model, which is a realistic model for bismuth, is studied. The inverse magnetoconductivity so obtained is not saturated, but is reduced at high fields. Implications of present results to the linear magnetoresistivity of bismuth are discussed.

We investigate the Meissner effect (ME) of Dirac electrons in a superconducting state on the basis of Kubo formula, and clarify that Meissner kernel becomes finite by use of the inter-band contribution. This mechanism of the ME for Dirac electron is completely different from that for the electron in the usual metals. We also derive the result of the electron gas by taking the non-relativistic limit of Dirac Hamiltonian, and clarify that the diamagnetic term of the Meissner kernel can be regarded as the inter-band contribution between electrons and positrons in terms of the Dirac model.

Based on the Keldysh Green's functions theory, we present a general formula of the thermal and thermoelectric transport. In the clean limit, our formula recovers the previous results obtained from the semiclassical transport theory. In our approach, we propose an appropriate energy current operator and electric current operator, and the unphysical divergence from the direct application of the Kubo formula is eliminated. As an application, we study the thermal and the thermoelectric Hall conductivities of a gapped Dirac fermion model in the presence of impurity scattering.