Conductivity of disordered 2d binodal Dirac electron gas: effect of internode scattering

We study the dc conductivity of a weakly disordered 2d Dirac electron gas with two bands and two spectral nodes, employing a field theoretical version of the Kubo–Greenwood conductivity formula. In this paper, we are concerned with the question how the internode scattering affects the conductivity. We use and compare two established techniques for treating the disorder scattering: The perturbation theory, there ladder and maximally crossed diagrams are summed up, and the functional integral approach. Both turn out to be entirely equivalent. For a large number of random potential configurations we have found only two different conductivity scenarios. Both scenarios appear independently of whether the disorder does or does not create the internode scattering. In particular, we do not confirm the conjecture that the internode scattering tends to Anderson localisation.     

Vertex correction and conductivity in 2D Dirac-like systems with non-conserving spin disorder

We determine the classical diffusion of two dimensional Dirac-like quasiparticles, in the presence of conserving spin disorder (scattering off electric impurities) and non-conserving spin disorder (scattering off magnetic impurities). We use the Kubo formula for the conductivity tensor and employ diagrammatic perturbation theory to calculate the vertex correction and the renormalisation of the current operator for both electric and magnetic scattering. Scattering off electric impurities is isotropic and the current operator renormalised to two times the bare current operator irrespective of the direction of the dynamics, as usual for Dirac-like fermions. For magnetic scattering the renormalisation of the current operator depends on the direction of the dynamics and on the polarisation of the magnetic impurities, making the system anisotropic. We calculate the anisotropic magnetoresistance (AMR) and analyse it as a function of the ratio of the strength of the electric to the magnetic scattering potentials, for short range Gaussian correlation.     

Hall conductivity for two-dimensional magnetic systems

A Kubo inspired formalism is proposed to compute the longitudinal and transverse dynamical conductivities of an electron in a plane (or a gas of electrons at zero temperature) coupled to the potential vector of an external local magnetic field, with the additional coupling of the spin degree of freedom of the electron to the local magnetic field (Pauli Hamiltonian). As an example, the homogeneous magnetic field Ha]] conductivity is rederived. The case of the vortex at the origin is worked out in detail. This system happens to display a transverse Ha]] conductivity (P breaking effect) which is subleading in volume compared to the homogeneous field case, but diverging at small frequencies like 1/ω². A perturbative analysis is proposed for the conductivity in the random magnetic impurity problem (Poissonian vortices in the plane). At first order in perturbation theory, the Ha]] conductivity displays oscillations close to the classical straight line conductivity of the mean magnetic field.     

The Hall coefficient of the small polaron

The Hall coefficient of the small polaron in theHolstein model suitably generalized to three dimensions and to the presence of a magnetic field is calculated by means of the Kubo formula. A perturbation expansion of the correlation function appearing in the Kubo formula is used to introduce higher order jumps of the polaron which are the first to be affected by the magnetic field. A general expression for the Hall coefficient is obtained which essentially coincides with the result ofFriedman andHolstein obtained for special cases. Moreover, it is shown that interference processes of thermal activation and free motion of the small polaron change the Hall effect, and their contribution to the value of the Hall coefficient is calculated.     

Hall Conductivity in a Quasi—Two—Dimensional disordered Electron System

By making use of the diagrammatic techniques in perturbation theory,we have investigated the Hall effect in a quasi-two dimensional disordered electron system.In the weakly localized regime,the analytical expression for quantum correction to Hall conductivity has been obtained using the kubo formalism and quasiclassical approximation.The relevant dimensional crossover behavior from three dimensions to two dimensions with decreasing the interlayer hopping energy is discussed.The quantum interference effect is shown to have a vanishing correction to the Hall coefficient.     

Non-Abelian Kubo Formula and the Multiple Time-Scale Method

The non-Abelian Kubo formula is derived from the kinetic theory. That expression is compared with the one obtained using the eikonal for a Chern–Simons theory. The multiple time-scale method is used to study the non-Abelian Kubo formula, and the damping rate for longitudinal color waves is computed.     

Landau–Khalatnikov–Fradkin Transformation and Even $$\zeta$$ Functions

Physics of Atomic Nuclei - An exact formula that relates standard $$\zeta$$ functions and so-called hatted $$\zeta$$ ( $$\hat{\zeta}$$ ) functions in all orders of perturbation theory is presented....     

Energy magnetization and the thermal Hall effect

We obtain a set of general formulas for determining magnetizations, including the usual electromagnetic magnetization as well as the gravitomagnetic energy magnetization. The magnetization corrections to the thermal transport coefficients are explicitly demonstrated. Our theory provides a systematic approach for properly evaluating the thermal transport coefficients of magnetic systems, eliminating the unphysical divergence from the direct application of the Kubo formula. For a noninteracting anomalous Hall system, the corrected thermal Hall conductivity obeys the Wiedemann-Franz law.     

The thermoelectric properties of the small polaron

The high temperature behaviour of the thermoelectric transport coefficients for the Holstein small polaron model is investigated. An expression for the energy flux operator is derived, which includes the flow of the electron-lattice interaction energy. This inclusion is necessary for the small polaron model, because the electron-phonon coupling is assumed to be strong, while the kinetic energy of the electrons is understood as a small perturbation. Kubo formulae are used and approximated in lowest order perturbation theory. It follows that there are no dynamical corrections to the thermoelectric power. But the strong electron-lattice interaction leads to a contribution to the thermal conductivity.     

Semiclassical spin transport in spin-orbit-coupled bands

Motivated by recent interest in novel spintronics effects, we develop a semiclassical theory of spin transport that is valid for spin-orbit coupled bands. Aside from the obvious convective term in which the average spin is transported at the wave packet group velocity, the spin current has additional contributions from the wave packet's spin and torque dipole moments. Electric field corrections to the group velocity and carrier spin contribute to the convective term. Summing all terms we obtain an expression for the intrinsic spin-Hall conductivity of a hole-doped semiconductor, which agrees with the Kubo formula prediction for the same quantity. We discuss the calculation of spin accumulation, which illustrates the importance of the torque dipole near the boundary of the system.     

Theory of the phonon Hall effect in paramagnetic dielectrics

Based upon Raman spin-lattice interaction, we propose a theoretical model for the phonon Hall effect in paramagnetic dielectrics, which was discovered recently in an experiment [C. Strohm, G. L. J. A. Rikken, and P. Wyder, Phys. Rev. Lett. 95, 155901 (2005).]. The phonon Hall effect is revealed to be a phonon analogue to the anomalous Hall effect in electron systems. The thermal Hall conductivity is calculated by using the Kubo formula. Our theory reproduces the essential experimental features of the phonon Hall effect, including the sign, magnitude, and linear magnetic field dependence of the thermal Hall conductivity.     

Spin transport in the two-dimensional anisotropic XY model coupled to phonons

In this paper, we study spin currents, generated by a magnetic field gradient, in the two-dimensional XY model with single-ion anisotropy and coupled to phonons in the large D phase. The spin conductivity is calculated, at zero temperature, using the Kubo formula.     

Comments on the equilibrium theory of the quantum hall effect

The relation between the thermal equilibrium Hall conductivity generated by minimal gauge transformation and the isolated Hall conductivity given by the Kubo formula is investigated. The contribution of the edge states and some general questions concerning the definition of the equilibrium Hall conductivity are discussed. It is shown that, in the case of an additive electron-impurity system, the two Hall conductivities coincide as long as the Fermi energy is situated in an energy gap.     

Quantum Hall conductivity in a Landau type model with a realistic geometry

In this paper, we revisit some quantum mechanical aspects related to the quantum Hall effect. We consider a Landau type model, paying a special attention to the experimental and geometrical features of quantum Hall experiments. The resulting formalism is then used to compute explicitely the Hall conductivity from a Kubo formula.     

金属薄膜的量子输运理论

运用格林函数方法和久保公式研究金属薄膜中的电子输运．考虑了量子尺寸效应及来自杂质和两个粗糙表面的散射，计算单粒子格林函数和平行电导率．计算结果表明：（1）在薄膜系统中，电子数密度、平均自由程以及来自杂质和表面散射的电导率都以π/k_F（k_F为费密波矢的数值）为周期随厚度d振荡；（2）在薄膜和厚膜的两种极限、以及取表面粗糙度的最低阶近似下的结果可以推出用半经典和量子方法所得的金属薄膜的电导公式 关键词：     

Optical conductivity in alloys: Optical effective mass

A generalized Kubo formula for the optical conductivity and the associated optical mass in alloys is derived for off-diagonal randomness and analyzed in the dilute limit. A possible resolution for the decrease in the optical mass upon alloying observed in certain dilute alloys is suggested.     

强磁场下的输运过程与Liouville方程的两种定态解

本文中讨论了在外场中Liouville方程的两种定态解,指出在用Kubo公式计算输运系数时的关键之处是:在完成Kubo公式中的时间积分之前,必须把关联函数的时间行为表示成趋向平衡的形式。注意到这一点就能得到正确的输运系数表示式。用这种办法,我们重新计算了文献[1]中曾讨论过的强磁场下的电导率,得到了正确的非零的结果。 关键词：     

Gravitational anomaly and transport phenomena

Quantum anomalies give rise to new transport phenomena. In particular, a magnetic field can induce an anomalous current via the chiral magnetic effect and a vortex in the relativistic fluid can also induce a current via the chiral vortical effect. The related transport coefficients can be calculated via Kubo formulas. We evaluate the Kubo formula for the anomalous vortical conductivity at weak coupling and show that it receives contributions proportional to the gravitational anomaly coefficient. The gravitational anomaly gives rise to an anomalous vortical effect even for an uncharged fluid.     

A diagram technique for perturbation theory calculations of the effective conductivity of two-dimensional systems

The perturbation theory for calculating the ffective conductivity of the plane consisting of pieces of different conductivities is constructed, and a convenient diagram technique is elaborated for this perturbation theory. It is shown that for the chessboard, perturbative calculations give results that are in agreement with the well-known formula $\sigma _{eff} = \sqrt {\sigma _1 \sigma _2 } $ . The components of the effective conductivity tensor for the anisotropic three-color chessboard are calculated. It is shown that the isotropic (symmetric) part of the effective conductivity calculated up to the sixth order of perturbation theory satisfies the Bruggeman effective medium equation for symmetric three-color structures with equally partitioned components. We also consider an isotropic three-color chessboard with nonequal weights of colors. In this case, the perturbation theory in the fourth order contradicts the results following from the Bruggeman equation for nonequal weights.