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Sizable Rashba spin-orbit coupling (SOC) is of critical importance in potential applications of two-dimensional materials in spintronics devices. However, due to the presence of vertical mirror symmetry, Rashba SOC is absent in 2H transition-metal dichalcogenide monolayers and the spin Hall conductivities are attributed only to Zeeman splitting. We study theoretically the electronic structures and intrinsic spin Hall conductivity of two-dimensional monolayer Janus MoSSe by performing first-principles calculations as well as by using the Kubo formula with Wannier interpolations. We find out that monolayer Janus MoSSe possesses considerable spin Hall conductivities both in conduction and valence bands. In valence bands, the spin Hall conductivity of Janus MoSSe is comparable to that in ${\mathrm{MoS}}_{2}$ and ${\mathrm{MoSe}}_{2}$. Moreover, in the conduction bands, the spin Hall conductivities are enhanced up to two orders of magnitude because of strong Rashba SOC. The spin Hall conductivity can be tuned significantly by adjusting the Fermi level or external strains. Our results show that monolayer Janus MoSSe could be a potential candidate to realize two-dimensional flexible spintronics devices.

Electronic properties of gapped graphene structure taking into account the effects of interaction between electrons and Einstein phonons have been addressed. Specially we study the temperature dependence of electrical conductivity and density of states of the structure. The effects of gap parameter, magnetic field and electron doping on electrical conductivity of the system have been studied. Gap parameter is defined as the on-site energy difference of atoms on two different sublattices of honeycomb structure. Green’s function method has been implemented to obtain electronic density of states of the system in the context of Holstein model Hamiltonian. One loop electronic self-energy of the model Hamiltonian has been obtained in order to find interacting electronic Green’s function. The electrical conductivity of graphene structure in the presence of electron-phonon coupling can be readily found using interacting Green’s function based on Kubo formula. We present the numerical results of energy dependence of density of states for different values of gap parameter and magnetic field in the presence of Holstein phonons. Finally the temperature dependence of electrical conductivity of gapped graphene structure due to electron phonon interaction and magnetic has been investigated. Our results show turning on magnetic field leads to appear double van Hov singularity for each value of electron phonon coupling.

Monolayer NbSe2 is a metallic two-dimensional (2D) transition-metal dichalcogenide material. Owing to the lattice structure and the strong atomic spin-orbit coupling (SOC) field, monolayer NbSe2 possesses Ising-type SOC which acts as effective Zeeman field, leading to the unconventional topological spin properties. In this paper, we numerically calculate spin-dependent optical conductivity of monolayer NbSe2 using Kubo formula based on an effective tight-binding model which includes $d_{z^2}$, $d_{x^2-y^2}$ and $d_{xy}$ orbitals of Nb atom. Numerical calculation indicates that the up- and down-spin have opposite sign of Hall current, so the pure spin Hall current can be generated in monolayer NbSe2 under light irradiation, owing to the topological nature of monolayer NbSe2, i.e., finite spin Berry curvature. The spin Hall angle is also evaluated. The optical induced spin Hall current can be enhanced by the electron doping and persists even at room temperature. Our results will serve to design opt-spintronics devices such as spin current harvesting by light irradiation on the basis of 2D materials., Comment: 4 pages, 3 figures

In this work, we explore macroscopic transport phenomena associated with a rotational system in the presence of an external orthogonal electromagnetic field. Simply based on the lowest Landau level approximation, we derive nontrivial expressions for chiral density and various currents consistently by adopting small angular velocity expansion or Kubo formula. While the generation of anomalous electric current is due to the pseudo gauge field effect of the spin-rotation coupling, the chiral density and current can be simply explained with the help of Lorentz boosts. Finally, Lorentz covariant forms can be obtained by unifying our results and the magnetovorticity effect.

In the present paper, we investigate the influence of a grounded perfectly conducting surface on the photon self-energy of a $2+1\mathrm{D}$ system of massless Dirac fermions, whose electron interaction is described by pseudoquantum electrodynamics. We calculate the temporal component of the polarization tensor up to 2-loop perturbation order in the presence of the conducting surface and, applying the Kubo formula, we obtain the longitudinal and optical conductivities of such system. When the distance between the system and the plate tends to infinity, we recover the correspondent results found in the literature. Since pseudoquantum electrodynamics proved to give a good description of the transport properties of graphene, our results can be useful as an alternative way to control the longitudinal and optical conductivities of this material.

We analytically study the electronic structure and optical properties of zigzag-edged phosphorene nanoribbons (ZPNRs) using the tight-binding Hamiltonian and Kubo formula. By directly solving the discrete Schrodinger equation, we obtain the energy spectra and wavefunctions for N-ZPNR (where TV is the number of transverse zigzag atomic chains) and classify the eigenstates according to the lattice symmetry. Then, we obtain the optical transition selection rule of ZPNRs on the basis of symmetry analysis and analytical expressions of optical transition matrix elements. Under incident light that is linearly polarized along the ribbon, we determine that the optical transition selection rule for N-ZPNR with even- or odd-N is qualitatively different. Specifically, for even-N ZPNRs, the inter- (intra-) band selection rule is An =odd (even) because the parity of the wavefunction corresponding to the n-th subband in the conduction (valence) band is (-1)n[(-1)(n+1)] owing to the presence of C2x symmetry. However, the optical transitions between any subbands are possible owing to the absence of C2x symmetry. Our results provide a further understanding on the electronic states and optical properties of ZPNRs, which are useful for explaining the optical experiment data on ZPNR samples.

We systematically investigate the anisotropic magneto-conductivity and planar Hall effect in tilted magnetic topological semimetals in the frame of Kubo formula by considering the vertex correction of velocity. The nonzero anisotropic magneto-conductivity is due to the intrinsic magnetization by magnetic doping rather than the external magnetic field previously studied in literatures. In the scenario, tilt, which is common in band structure, plays a key role in this anisotropic magneto-conductivity. This anisotropic magneto-conductivity completely originates from the band anisotropy. The vertex correction only amends the magnitude, but does not change the qualitative behavior of the longitudinal conductivity. However, the planar Hall conductivity is always zero for tilt along both x and y directions in vivid contrast to the case arising from an external magnetic field. Our work offers a route to understand the anisotropic magneto-conductivity effect in tilted Weyl semimetals with Zeeman field. It will be helpful to get a deeper understanding of the transport characteristic in tilted topological semimetals.

Monolayer transition metal dichalcogenides (TMDCs) under the application of a magnetic exchange field carry the nontrivial optical Hall conductivity and thus exhibit the nonzero Faraday rotation (FR) angle. However, the tradeoff between the FR angle and transmission hinders their possible applications in magnetic-optical (MO) devices. Here, we theoretically show that a heterostructure of two photonic crystals with proximitized monolayer TMDCs enables the enhancement of the FR angle and transmission simultaneously through the combination of a four-band Hamiltonian model, Kubo formula and transfer matrix method. The MO improvement in the hybrid structure in both the FR angle and transmission is determined by the combined effects from the localized electromagnetic field at the interface between the two photonic crystals and the satisfaction of the phase match condition. Our work opens up an alternative opportunity to use TMDCs in two-dimensional MO fields in the visible frequency range.

The study on the electronic especially optical properties of zigzag-edged phosphorene nanoribbons (ZPNRs) in an antiferromagnetic state has been rarely involved. Here we theoretically study the electronic and optical properties of a ZPNR with N chains ( N -ZPNR) modulated by a vertical electric field (VEF). Within the Hubbard model Hamiltonian combined with the self-consistent calculation, and by adopting the Green’s function method, we obtain the band structure and corresponding conductance for the system. The corresponding optical absorption spectrum is further obtained based on the Kubo formula. It is interesting to find that there is an even–odd effect on the electronic and optical properties of N -ZPNR induced by the VEF, which may fundamentally originate from the parity of the wavefunctions. The VEF lifts the degeneracy of the two edge bands for 12-ZPNR, but it only bends and shifts the two edge bands without lifting the spin degeneracy for 13-ZPNR. We further present the spatial distribution of the corresponding wavefunction to understand this even–odd effect more intuitively. As expected, the VEF can separate the spin-up and -down optical absorption for 12-ZPNR, but it does not break the spin degeneracy of the optical absorption for 13-ZPNR. Our results may provide a further understanding on the electronic and optical properties of N -ZPNR with an antiferromagnetic state, and may be useful to identify the even–odd property of ZPNR samples by detecting the optical absorption in experiment.

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.

The electronic structures of two-dimensional hexagonal materials for a given spin direction can be generally written by the Haldane model, which shows circular dichroism or valley polarization due to broken time-reversal and inversion symmetries, respectively. By using the Kubo formula, we calculate longitudinal and transversal (Hall) optical conductivities to obtain the absorption spectra. The absorption spectra for circularly polarized lights are calculated by solving the Maxwell equations with a boundary conditions at the two-dimensional material. We found that circular dichroism and valley polarization depend on the properties of the imaginary part of the Hall conductivity, while the real part of the Hall conductivity generates large Faraday and Kerr rotations up to a few degrees.

We study a model of a quantum dot coupled to a quantum Hall edge of the Laughlin state, taking into account short-range interactions between the dot and the edge. This system has been studied experimentally in electron quantum optics in the context of single particle sources. We consider driving the dot out of equilibrium by a time-dependent bias voltage. We calculate the resulting current on the edge by applying the Kubo formula to the bosonized Hamiltonian. The Hamiltonian of this system can also be mapped to the spin-boson model and in this picture, the current can be perturbatively calculated using the non-interacting blip approximation (NIBA). We show that both methods of solution are in fact equivalent. We present numerics demonstrating that the perturbative approaches capture the essential physics at early times, although they fail to capture the charge quantization (or lack thereof) in the current pulses integrated over long times., Comment: 10 pages, 2 figures, accepted version

The performance of a newly designed multi-layered parallel plate waveguide (PPWG), supported by two, three and four graphene plates, is evaluated here. The graphene layers used for this study were biased with both electric and magnetic fields. The graphene plates behavior was modeled as an anisotropic medium, with both diagonal and Hall conductivities derived from the Kubo formula. Maxwells equations were solved for these waveguides; and it is shown, here, that when both electric and magnetic biases were applied to the graphene, hybrid modes (simultaneous transverse electric (TE) and transverse magnetic (TM) modes) propagated inside the waveguides. The intensity of each TE and TM mode could be adjusted with an applied external field bias. This feature is valuable for various applications, such as converting TE modes to TM modes, and vice versa. In addition, due to the anisotropic properties of graphene walls, PPWGs with graphene walls under magnetic field biases are applicable to the design of non-reciprocal devices, such as isolators, circulators and one-way couplers. This study of wave confinement has shown that, by varying the bias, full control can be exerted over the waves propagation within a waveguide; whereby, increasing the bias causes added phase changes over the propagation length, while increasing the waveguides attenuation. This full control would also be helpful when using the waveguide structure to design numerous devices, such as switches, couplers, attenuators and modulators. It must be emphasized that the presented analytical procedure is also applicable to other guiding structures that have walls with isotropic or anisotropic conductivities.

We study the dynamic chiral magnetic conductivity (DCMC) and natural optical activity in an inversion-broken tilted Weyl semimetal (WSM). Starting from the Kubo formula, we derive the analytical expressions for the DCMC for two different directions of the incident electromagnetic wave. We show that the angle of rotation of the plane of polarization of the transmitted wave exhibits remarkable anisotropy and is larger along the tilt direction. This striking anisotropy of DCMC results in anisotropic optical activity and rotary power, which can be experimentally observed as a topological magneto-electric effect of inversion-broken tilted WSMs. Finally, using the low energy Hamiltonian, we show that the DCMC follows the universal $$\frac{{\bf{1}}}{{{\boldsymbol{\omega }}}^{{\bf{2}}}}$$ 1 ω 2 decay in the high frequency regime. In the low frequency regime, however, the DCMC shows sharp peaks at the tilt dependent effective chemical potentials of the left-handed and right-handed Weyl points. This can serve as a signature to distinguish between the type-I and type-II Weyl semimetals.

For an isotropic single-band system, it is well known that the semiclassical Boltzmann transport theory within the relaxation time approximation and the Kubo formula with the vertex corrections provide the same result with the $(1-\cos\theta)$ factor in the inverse transport relaxation time. In anisotropic multiband systems, the semiclassical Boltzmann transport equation is generalized to coupled integral equations relating transport relaxation times at different angles in different bands. Using the Kubo formula, we study the vertex corrections to the dc conductivity in anisotropic multiband systems and derive the relation satisfied by the transport relaxation time for both elastic and inelastic scatterings, verifying that the result is consistent with the semiclassical approach., Comment: 11 pages, 7 figures

We compute the optical conductivity of gapped graphene taking into account the effects of interaction between electrons and Einstein phonons beyond the usual Dirac-cone approximation. Our study is based on the Kubo formula that is established upon the retarded self-energy. Specially we report the frequency dependence of optical absorption of the structure. We find numerical results for frequency dependence of optical absorption for different values of gap parameter in the presence of Holstein phonons. We have also studied the effects of electron-phonon coupling strength and electronic concentration on the behavior of optical absorption of the gapped graphene structure. Our results show the increase of electronic chemical potential in doped case leads to appear optical band gap in the structure. This optical gap arises from Pauli blocking of vertical transitions when conduction band is doped. Electron-phonon coupling broadens the peak in the optical spectral and decreases the intensity of optical absorption. However the frequency position of the peak is not considerably affected by electron-phonon coupling.

We study the conductivity of two-dimensional graphene-type materials with tilted cones as well as their three-dimensional Weyl counterparts and show that a covariant quantum Boltzmann equation is capable of providing an accurate description of these materials' transport properties. The validity of the covariant Boltzmann approach is corroborated by calculations within the Kubo formula. We find a strong anisotropy in the conductivities parallel and perpendicular to the tilt direction upon increase of the tilt parameter $\eta$, which can be interpreted as the boost parameter of a Lorentz transformation. While the ratio between the two conductivities is $\sqrt{1-\eta^2}$ in the two-dimensional case where only the conductivity perpendicular to the tilt direction diverges for $\eta\rightarrow 1$, both conductivities diverge in three-dimensional Weyl semimetals, where $\eta=1$ separates a type-I (for $\eta1$)., Comment: 14 pages, 9 figures

Structural defects are inherent in solids at a finite temperature, because they diminish free energies by growing entropy. The arrangement of these defects may display long-range orders, as occurring in quasicrystals, whose hidden structural symmetry could greatly modify the transport of excitations. Moreover, the presence of such defects breaks the translational symmetry and collapses the reciprocal lattice, which has been a standard technique in solid-state physics. An alternative to address such a structural disorder is the real space theory. Nonetheless, solving 1023 coupled Schrödinger equations requires unavailable yottabytes (YB) of memory just for recording the atomic positions. In contrast, the real-space renormalization method (RSRM) uses an iterative procedure with a small number of effective sites in each step, and exponentially lessens the degrees of freedom, but keeps their participation in the final results. In this article, we review aperiodic atomic arrangements with hierarchical symmetry investigated by means of RSRM, as well as their consequences in measurable physical properties, such as electrical and thermal conductivities.

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.

This thesis predicts that two types of material families could be a solution to the challenges in spintronics: complex oxides and bismuth based materials. We derive a general approach for constructing an effective spin-orbit Hamiltonian, which applies to all nonmagnetic materials. We also verify this formalism through comparisons with other approaches for III-V semiconductors. Its general applicability is illustrated by deriving the spin-orbit interaction and predicting spin lifetimes for strained SrTiO$_3$ and a two-dimensional electron gas (such as at the LaAlO$_3$/SrTiO$_3$ interface). Our results suggest robust spin coherence and spin transport properties in SrTiO$_3$ related materials. In the second part, we calculate intrinsic spin Hall conductivities for Bi$_{1-x}$Sb$_x$ semimetals with strong spin-orbit couplings, from the Kubo formula and using Berry curvatures evaluated from a tight-binding Hamiltonian. Nearly crossing bands with strong spin-orbit interaction generate giant spin Hall conductivities in these materials, ranging from 474 ($\hbar/e)( \Omega^{-1}cm^{-1}$) for bismuth to 96($\hbar/e)( \Omega^{-1}cm^{-1}$) for antimony; the value for bismuth is more than twice that of platinum. The large spin Hall conductivities persist for alloy compositions corresponding to a three-dimensional topological insulator state, such as Bi$_{0.83}$Sb$_{0.17}$. The spin Hall conductivity could be changed by a factor of 5 for doped Bi, or for Bi$_{0.83}$Sb$_{0.17}$, by changing the chemical potential, suggesting the potential for doping or voltage tuned spin Hall current. We also calculate intrinsic spin Hall conductivities of Bi$_2$Se$_3$ and Bi$_2$Te$_3$ topological insulators from an effective tight-binding Hamiltonian. We conclude that bismuth-antimony alloys and bismuth chalcogenides are primary candidates for efficiently generating spin currents through the spin Hall effect.

Graphene is a promising carbon nanomaterial, and multilayer graphene are more interesting than the monolayer one. The dispersion of multilayer graphene at terahertz (THz) leads to difficulties in transient electromagnetic simulation, e.g. the time domain integral equation (TDIE) method. This paper aims to achieve accurate fitting of multilayer graphene dispersive surface conductivity/impedance over ultra wideband THz frequencies. Graphene surface conductivity/impedance at THz is calculated by the Kubo formula. Thereafter, the surface conductivity and impedance is approximated by vector fitting method with expansions of several pairs of poles and residues. Numerical results are provided to validate the proposed method. Multilayer graphene time domain surface impedance which is used in the impedance boundary condition (IBC) for TDIE can be obtained readily by the inverse Fourier transform of its frequency domain counterpart.

A formula for the Hall response of interacting multi-band systems with arbitrary band topology and spin-orbit coupling is derived. The formula is valid at finite frequency, which is relevant for Faraday rotation, and it takes into account all particle-hole vertex corrections. The formula includes both three-leg (triangular) and four-leg (rectangular) diagrams. The latter diagrams are absent in the single band case. We show that the rectangular diagrams are necessary to recover the semiclassical formula for the Hall effect from the Kubo formula in the DC limit. They also give the linear response of the anomalous Hall effect to an external magnetic field, an effect which goes beyond the semiclassical theory. Three- and four-particle scatterings are neglected., Comment: LaTex, 3 figures, 16 pages

A mathematical formulation for particle states and electronic properties of a curved graphene sheet is provided, exploiting a massless Dirac spectrum description for charge carriers living in a curved bidimensional background. In particular, we study how the new description affects the characteristics of the sample, writing an appropriate conductivity Kubo formula for the modified background. Finally, we provide a theoretical analysis for the particular case of a cylindrical graphene sample., 23 pages, 5 figures

Fermions with one and two Dirac nodes are coupled to in-plane phonons to study a spontaneous transition into the Hall insulating phase. At sufficiently strong electron–phonon interaction a gap appears in the spectrum of fermions, signaling a transition into a phase with spontaneously broken parity and time-reversal symmetry. The structure of elementary excitations above the gap in the corresponding phase reveals the presence of scale invariant parity breaking terms which resemble Chern–Simons excitations. Evaluating the Kubo formula for both models we find quantized Hall plateaux in each case, with conductance of binodal model exactly twice as large as of the mononodal model.

The intrinsic spin Hall conductivity of a two-dimensional gas confined to SrTiO$_3$, such as occurs at an LaAlO$_3$/SrTiO$_3$ interface, is calculated from the Kubo formula. The effect of strain in the [001] (normal to the quantum well direction) and the [111] direction is incorporated into a full tight-binding Hamiltonian. We show that the spin-charge conversion ratio can be significantly altered through strain and gate voltage by tuning the chemical potential. Strain direction is also a significant factor in the spin Hall response as this direction affects the alignment of the conduction bands., 9 pages, 6 figures

In this work, we show that the disorder-free Kubo formula for the non-equilibrium value of an observable due to a DC electric field, represented by $E_x\hat{x}$ in the Hamiltonian, can be interpreted as the standard time-independent theory response of the observable due to a time- and position-\textit{independent} perturbation $H_{MF}$. We derive the explicit expression for $H_{MF}$ and show that it originates from the adiabatic approximation to $\langle k|E_x\hat{x}$ in which transitions between the different eigenspinor states of a system are forbidden. The expression for $H_{MF}$ is generalized beyond the real spin degree of freedom to include other spin-like discrete degrees of freedom (e.g. valley and pseudospin). By direct comparison between Kubo formula and the time-independent perturbation theory, as well as the Sundaram-Niu wavepacket formalism, we show that $H_{MF}$ reproduces the effect of the E-field, i.e. $E_x\hat{x}$, up to the first order. This replacement suggests the emergence of a new spin current term that is not captured by the standard Kubo formula spin current calculation. We illustrate this via the exemplary spin current for the heavy hole spin 3/2 Luttinger system. Finally, we apply the formalism and derive an analogous $H_{MF}$ for the effects of a weakly position-dependent coupling to the spin-like internal degrees of freedom. This gives rise to an anomalous velocity as well as spin accumulation terms in spin$\otimes$pseudospin space in addition to those contained explicitly in the unperturbed Hamiltonian.

We study a weakly disordered 2D electron gas with two bands and a spectral node within the weak-localization approach and compare its results with those of Gaussian fluctuations around the self-consistent Born approximation. The appearance of diffusive modes depends on the type of disorder. In particular, we find for a random gap a diffusive mode only from ladder contributions, whereas for a random scalar potential the diffusive mode is created by ladder and by maximally crossed contributions. The ladder (maximally crossed) contributions correspond to fermionic (bosonic) Gaussian fluctuations. We calculate the conductivity corrections from the density--density Kubo formula and find a good agreement with the experimentally observed V-shape conductivity of graphene., 10 pages, 2 figures

We begin with a brief description of the role of the Nernst-Ettingshausen effect in the studies of the high-temperature superconductors and Dirac materials such as graphene. The theoretical analysis of the NE effect is involved because the standard Kubo formalism has to be modified by the presence of magnetization currents in order to satisfy the third law of thermodynamics. A new generation of the low-buckled Dirac materials is expected to have a strong spin Nernst effect that represents the spintronics analog of the NE effect. These Dirac materials can be considered as made of two independent electron subsystems of the two-component gapped Dirac fermions. For each subsystem the gap breaks a time-reversal symmetry and thus plays a role of an effective magnetic field. We explicitly demonstrate how the correct thermoelectric coefficient emerges both by the explicit calculation of the magnetization and by a formal cancelation in the modified Kubo formula. We conclude by showing that the nontrivial dependences of the spin Nersnt signal on the carrier concentration and electric field applied are expected in silicene and other low-buckled Dirac materials.

In this paper, we discuss the effect of a periodically driving circularly polarized laser beam in the high frequency limit, on the band structure and thermal transport properties of type-I and type-II Weyl semimetals (WSMs). We develop the notion of an effective Fermi surface stemming from the time-averaged Floquet Hamiltonian and discuss its effects on the steady-state occupation numbers of electrons and holes in the linearized model. In order to compute the transport coefficients averaged over a period of the incident laser source, we employ the Kubo formalism for Floquet states and show that the Kubo formula for the conductivity tensor retains its well known form with the difference that the eigenstates and energies are replaced by the Floquet states and their quasi-energies. We find that for type-I WSMs the anomalous thermal Hall conductivity grows quadratically with the amplitude $A_{0}$ of the U(1) gauge field for low tilt, while the Nernst conductivity remains unaffected. For type-II WSMs, the Hall conductivity decreases non-linearly with $A_{0}$ due to the contribution from the physical momentum cutoff, required to keep finite electron and hole pocket sizes, and the Nernst conductivity falls of logarithmically with $A_{0}^2$. These results may serve as a diagnostic for material characterization and transport parameter tunability in WSMs, which are currently the subject of a wide range of experiments., Comment: Accepted to PRB, 6 pages, 8 figures, 6 pages of supplementary material

Exact formulas for the Hall coefficient, modified Nernst coefficient, and thermal Hall coefficient of metals are derived from the Kubo formula. These coefficients depend exclusively on equilibrium (time independent) susceptibilities, which are significantly easier to compute than conductivities. For weak isotropic scattering, Boltzmann theory is recovered. For strong scattering, well controlled methods for thermodynamic functions are available. As an example, the Hall sign reversals of lattice bosons near the Mott insulator phases are determined. Appendices include mathematical supplements and instructions for calculating the coefficients., Comment: 19 pages, 5 figures. arXiv admin note: text overlap with arXiv:1802.04810

Ab initio calculation of intrinsic spin Hall conductivity (SHC) generally requires a strict convergence criterion and a dense $k$-point mesh to sample the Brillouin zone, making its convergence challenging and time consuming. Here we present a scheme for efficiently and accurately calculating SHC based on the maximally localized Wannier function (MLWF). The quantities needed by the Kubo formula of SHC are derived in the space of the MLWF and it is shown that only the Hamiltonian, the overlap, and the spin operator matrices are required from the initial ab initio calculation. The computation of these matrices and the interpolation of the Kubo formula on a dense $k$-point mesh can be easily achieved. We validate our results by prototypical calculations on fcc Pt and GaAs, which demonstrate that the Wannier interpolation approach is of high accuracy and efficiency. Calculations of $\ensuremath{\alpha}\text{\ensuremath{-}}\mathrm{Ta}$ and $\ensuremath{\beta}\text{\ensuremath{-}}\mathrm{Ta}$ show that SHC of $\ensuremath{\beta}\text{\ensuremath{-}}\mathrm{Ta}$ is 2.7 times that of $\ensuremath{\alpha}\text{\ensuremath{-}}\mathrm{Ta}$, while both have the opposite sign relative to fcc Pt and are an order of magnitude smaller than Pt. The calculated spin Hall angle of $\ensuremath{-}0.156$ is quite consistent with previous experiments on $\ensuremath{\beta}\text{\ensuremath{-}}\mathrm{Ta}$, further suggesting intrinsic contribution may dominate in $\ensuremath{\beta}\text{\ensuremath{-}}\mathrm{Ta}$. Our approach could facilitate large-scale SHC calculations and may benefit the discovery of materials with high intrinsic SHC.

We study spin torques induced by Rashba spin-orbit coupling in two-dimensional ferromagnets under the good-metal condition $\epsilon_{F}\tau/\hbar\gg1$ ($\epsilon_{F}$ the Fermi energy, $\tau$ the electron lifetime) by employing the Kubo formula. We find that, in the presence of spin-dependent disorder the Rashba torque changes greatly as the system evolves out of the weak disorder limit where $\hbar/\tau$ is much smaller than any intrinsic energy scale characterizing the multiband structure. The antidamping-like component of Rashba torque can be comparable to and larger than the field-like one out of the weak disorder limit. The semiclassical Boltzmann theory produces the same results as microscopic linear response calculations only in the weak disorder limit. Our analysis indicates that rich behaviors of various nonequilibrium phenomena beyond the Boltzmann theory may also be present even when $\epsilon_{F}\tau/\hbar\gg1$ in multiband systems where $\epsilon_{F}$ is not the unique intrinsic energy scale., Comment: 6 pages, 2 figures

This paper considers a model consisting of a kinetic term, Rashba spin-orbit coupling and short-range Coulomb interaction at zero-temperature. The Coulomb interaction is decoupled by a mean-field approximation in the spin channel using field theory methods. The results feature a first-order phase transition for any finite value of the chemical potential and quantum criticality for vanishing chemical potential. The Hall conductivity is also computed using Kubo formula in a mean-field effective Hamiltonian. In the limit of infinite mass the kinetic term vanishes and all the phase transitions are of second order, in this case spontaneous symmetry breaking mechanism adds a ferromagnetic metallic phase to the system and features a zero-temperature quantization of the Hall conductivity in the insulating one., 7 pages, 6 figures. Version 3: published version

We study how the synergetic effect of spin-orbit coupling (SOC) and Zeeman splitting (ZS) affects the optical conductivity in the one-dimensional Hubbard model using the Kubo formula. We focus on two phenomena: (1) the electric dipole spin resonance (EDSR) in the metallic regime and (2) the optical conductivity in the Mott-insulating phase above the optical gap. In both cases, we calculate qualitatively the effects of SOC and ZS and how they depend on the relative angle between the SOC vector and the magnetic field direction. First, we investigate the spin resonance without electron correlation (the Hubbard parameter $U=0$). Although, neither SOC nor ZS causes any resonance by itself in the optical conductivity, the EDSR becomes possible when both of them exist. The resulting contribution to the optical conductivity is analyzed analytically. The effect of $U$ on the spin resonance is also studied with a numerical method. It is found that at half-filling, the resonance is first enhanced for small $U$ and then suppressed when the optical gap is large enough. In the strong coupling limit $U \rightarrow \infty$ at half-filling, we also refer to the resonance between the lower and upper Hubbard bands appearing at $\omega \sim U$, above the optical gap. A large magnetic field tends to suppress the signal while it is recovered thanks to SOC depending on the relative angle of the magnetic field., Comment: 8 pages, 7 figures

A non-contact method is proposed to characterize graphene at microwave frequency by combining Raman spectroscopy and Amphenol Precision Connector (APC-7). The CVD-grown graphene is transferred to the ring-shape Teflon substrate and characterized by Raman spectroscopy to estimate its doping density and the related Fermi energy. The graphene is then sandwiched between two APC-7 coaxial connectors and S parameters under transverse electromagnetic (TEM) mode normal incident waves are measured to extract the surface conductivity through transmission matrix, in which the de-embedding process can be avoided. By combing the Kubo formula with our proposed circuit model, the scattering rate of graphene on Teflon substrate is obtained and analyzed.

It is well known that future information technology relies upon electronic states other than charge, through the feasibility of constructing spintronic and valleytronic devices. The main challenge in such applications is the generation and control of the corresponding state currents. The present paper is thus concerned with charge, spin and valley currents which intrinsically develop in armchair silicene nanoribbons (ASNs). In pursuing this consideration the well established Kubo formula is employed. Taking the symmetries of the ASN into account, we analyze the structure of total Hamiltonian and demonstrate how the matrix elements along with the summations involved in the suitably adopted Kubo formula, may be analytically calculated. The results so-obtained along with the corresponding figures reveal that all three currents develop in a step-wise manner. The heights, indicating a jump in the current, and the plateaus, indicating a constant current, are shown to be tunable by adjusting the width and/or the buckled effect. Moreover, we demonstrate that for particular (critical) widths an inversion in band gaps may occur, giving rise to quantum phase transitions. More practical result of this paper, as we show, is the fact that the ASN can generate pure spin or valley current under specific conditions placed on the width, buckled effect and Fermi energy. The material presented in this paper thus provides novel means of generation and control of the charge, spin and valley currents.

We investigate theoretically the linear dichroism and the Faraday rotation of strained few-layer phosphorene, where strain is applied uniaxially along the armchair or zigzag direction of the phosphorene lattice. We calculate the optical conductivity tensor of uniaxially strained few-layer phosphorene by means of the Kubo formula within the tight-binding approach. We show that the linear dichroism and the Faraday rotation of few-layer phosphorene can be significantly modulated by the applied strain. The modulation depends strongly on both the magnitude and direction of strain and becomes more pronounced with increasing number of phosphorene layers. Our results are relevant for mechano-optoelectronic applications based on optical absorption and Hall effects in strained few-layer phosphorene.

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.

The coupled kinetic equation for density and spin Wigner functions is derived including spin-orbit coupling, electric and magnetic fields, and self-consistent Hartree mean fields suited for SU(2) transport. The interactions are assumed to be with scalar and magnetic impurities as well as scalar and spin-flip potentials among the particles. The spin-orbit interaction is used in a form suitable for solid state physics with Rashba or Dresselhaus coupling, graphene, extrinsic spin-orbit coupling, and effective nuclear matter coupling. The deficiencies of the two-fluid model are worked out consisting of the appearance of an effective in-medium spin precession. The stationary solution of all these systems shows a band splitting controlled by an effective medium-dependent Zeeman field. The self-consistent precession direction is discussed and a cancellation of linear spin-orbit coupling at zero temperature is reported. The precession of spin around this effective direction caused by spin-orbit coupling leads to anomalous charge and spin currents in an electric field. Anomalous Hall conductivity is shown to consist of the known results obtained from the Kubo formula or Berry phases and a symmetric part interpreted as an inverse Hall effect. Analogously the spin-Hall and inverse spin-Hall effects of spin currents are discussed which are present even without magnetic fields showing a spin accumulation triggered by currents. The analytical dynamical expressions for zero temperature are derived and discussed in dependence on the magnetic field and effective magnetizations. The anomalous Hall and spin-Hall effect changes sign at higher than a critical frequency dependent on the relaxation time.

In this methodology focused paper we scrutinize the application of the band-coherent Boltzmann equation approach to calculating the conductivity of chiral particles. As the ideal testing ground we use the two-band kinetic Hamiltonian with an N-fold chiral twist that arise in a low-energy description of charge carriers in rhombohedrally stacked multilayer graphene. To understand the role of chirality in the conductivity of such particles we also consider the artificial model with the chiral winding number decoupled from the power of the dispersion. We first utilize the approximate but analytically solvable band-coherent Boltzmann approach including the ill-understood principal value terms that are a byproduct of several quantum-many body theory derivations of Boltzmann collision integrals. Further on, we employ the finite-size Kubo formula with the exact diagonalization of the total Hamiltonian perturbed by disorder. Finally, we compare several choices of Ansatz in the derivation of the Boltzmann equation according to the qualitative agreement between the Boltzmann and Kubo conductivities. We find that the best agreement can be reached in the approach where the principle value terms in the collision integral are absent., 21 pages, 5 figures

Graphene is different from most optical materials in that it is a thin material layer with a thickness as small as one atom. Graphene layers can be incorporated into optical simulations using either a surface conductivity material model or a volumetric permittivity material model; however, introducing graphene through a volumetric permittivity is computationally inefficient because it requires very fine discretization grids. We have recently developed a more efficient approach that enables the use of comparatively coarse grids by formulating a discretization of Maxwell’s equations (in the time or frequency domains) that combines a surface conductivity description of graphene layers with a volumetric permittivity description of other optical materials. This approach includes the full dispersion characteristics of graphene as specified by the Kubo formula. This paper demonstrates how the combined material description approach can be used to efficiently model state-of-the-art devices that take advantage of the energy confinement provided by surface plasmons. We show how to efficiently model TE and TM polarized surface plasmons, a surface plasmon waveguide switch, and an electro-optical modulator. This last example also includes electrical simulations of graphene and demonstrates how both optical and electrical simulations can be combined to produce a complete model of a graphene based device. For each example, we compare with previously published results, including experimental results.

The current density jB induced in a clean metal by a slowly-varying magnetic field B is formulated as the low-frequency limit of natural optical activity, or natural gyrotropy. Working with a multiband Pauli Hamiltonian, we obtain from the Kubo formula a simple expression for αGMEij=jBi/Bj in terms of the intrinsic magnetic moment (orbital plus spin) of the Bloch electrons on the Fermi surface. An alternate semiclassical derivation provides an intuitive picture of the effect, and takes into account the influence of scattering processes in dirty metals. This “gyrotropic magnetic effect” is fundamentally different from the chiral magnetic effect driven by the chiral anomaly and governed by the Berry curvature on the Fermi surface, and the two effects are compared for a minimal model of a Weyl semimetal. Like the Berry curvature, the intrinsic magnetic moment should be regarded as a basic ingredient in the Fermi-liquid description of transport in broken-symmetry metals., We acknowledge support from Grant No. NSF DMR-1507141 (S. Z.), from the DOE LBL Quantum Materials Program and Simons Foundation (J. E. M.), and from Grants No. MAT2012-33720 from the Spanish Ministerio de Economía y Competitividad and No. CIG-303602 from the European Commission (I. S.).

In this work, we derive the analytical expression of the energy dispersions and minimal conductivity of the Bernal multilayer graphenes with the trigonal warping γ3 taken into consideration. Under unitary transformation, both the Hamiltonian matrix H and current operator ∂H/∂k of an N-layer Bernal graphene can be exactly reduced to block diagonal matrices. As the layer number N is even (odd), the 2N × 2N matrix is decomposed into N/2 four by four blocks (one 2 × 2 and (N–1)/2 4 × 4 blocks). Each of the Hamiltonian blocks represents an independent subsystem, which is an equivalent bilayer or a monolayer graphene. The analytical expression of energy dispersions are then obtained. Most importantly, the minimal conductivity, based on the Kubo formula, of Bernal multilayer graphene is equal to the summation of the direct current conductivity of each subsystem. The analytical formula of minimal conductivity is (N/2) 24/π (e2/h) [4/π(e2/h) + ((N – 1)/2)24/π(e2/h)] for even (odd) N, where 24/π (e2/h) is the condu...

Recently there has been an increasing interest in using organic materials for thermoelectric applications due to the noteworthy advantages of mechanical flexibility, low-cost synthesis, and solution processability. While the thermal conductivity of organic semiconductors is known to be small, very few theoretical works are available to predict thermoelectric properties of organic semiconductors and guide experimental efforts. In this work, we studied the thermoelectric properties (electrical conductivity, Seebeck coefficient, and power factor) of quasi-one-dimensional (Q1D) self-assembled molecular nanowires (NWs) based on a rigorous evaluation of the Kubo formula using the Holstein model. The molecular NWs are composed of either one-dimensional conducting polymer chains, coupled by covalent bonds, or linear stacks of planar building blocks, held together by van der Waals or π–π interactions; these are also known as molecule metals (or semiconductors), charge transfer salts, or π-stacked organic semicondu...

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.

The influence of inter unit cell resonant tunneling between the copper-oxygen planes on the c-axis electronic conductivity (σc) in normal state of optimal doped bilayer high Tc cuprates like Bi2Sr2CaCu2O8+x is investigated using extended Hubbard Hamiltonian including resonant tunneling term (T12) between the planes in two adjoining cells. The expression for the out-of-plane (c-axis) conductivity is calculated within Kubo formalism and single particle Green's function by employing Green's function equations of motion technique within meanfield approximation. On the basis of numerical computation, it is pointed out that the renormalized c-axis conductivity \((\tilde {\sigma}_{c})\) increases exponentially with the increment in inter cell resonant tunneling. The effect of T12 on renormalized c-axis conductivity is found to be prominent at low temperatures as compared to temperatures above room temperature (~300 °K). The Coulomb correlation suppresses the variation of renormalized c-axis conductivity with temperature, while renormalized c-axis conductivity increases on increasing carrier concentration. These theoretical results are viewed in terms of existing c-axis transport measurements.

We calculate shear viscosity of the quark matter at finite temperature and density. If we assume that the quark interacts with the soft mode, which is a collective mode of quark-antiquark pair, the self energy of the quark is calculated by using the quasi-particle random phase approximation. It is shown that its imaginary part is large and the mean free path of the quark is short. With the use of the Kubo formula, the shear viscosity of quark matter becomes small. The Reynolds number of the quark matter is estimated to be about $3\sim 30$. As the temperature increases, the shear viscosity increases gradually for $T>200{\rm MeV}$. Moreover it is shown that the shear viscosity is not sensitive to the chemical potential., 8 pages, 11 figures

We study the diffusion coefficient of Active Brownian particles in two dimensions. In addition to usual attributes of active motion we let the particles turn in preferred directions over random times. This angular motion is modeled by an effective Lorentz force with time dependent frequency switching between two values at exponentially distributed random times. The diffusion coefficient is calculated by the Taylor-Kubo formula where distributions found from a Fokker-Planck equation or from a continuous time random walk approach have been inserted for averaging. Eventually properties of the diffusion coefficient will be discussed.

Excitation and propagation of surface plasmons in intrinsic and extrinsic graphene are analyzed from the fundamental point of view, using time-dependent density functional theory in linear response regime. Density functional calculations, being set up from first principles, do include anisotropic effects in the unique electronic structure of graphene that cause remarkable consequences even on the THz band. The main signature of this anisotropy is the occurrence of two distinct plasmon modes over a frequency range of 1 to 300 THz, where most photonic devices currently operate with large bandwidths and low losses. Further anisotropic features are inherent to the different electromagnetic response of graphene to positive and negative doping concentrations. The Dirac-cone approximation provides a simplified insight, assuming an isotropic graphene band structure near the Fermi level, which is found to be reliable at probing frequencies below \(\sim 20\) THz and doping levels associated to Fermi energy shifts below/above ±0. 3 eV. In these limits, a continuous integral expression derived from the Kubo formula represents an easy-to-use tool capable of catching the main essence of the process.

It is well-known that liquid caesium shows some unusual properties at low densities. We used supercell technique within linear muffin-tin orbital method to investigate this phenomenon. Electronic structure of liquid caesium for different temperatures from the melting point up to critical point was obtained. The atomic structure was simulated for a cluster of 2000 atoms by the Reatto method on the base of experimental structure factors of Cs obtained by Winter and co-workers for different temperatures (from 323 K up to 1923 K). The Kubo-Greenwood formula was applied for the calculations of melts conductivity. The received results indicate that metal-nonmetal transition in liquid cesium is connected not to the gap at Fermi energy in density of electronic states, but more likely with electrons localization on some kind of atomic clusters. © 2007 Elsevier B.V. All rights reserved.