Kinetic theory of spin-polarized systems in electric and magnetic fields with spin-orbit coupling. I. Kinetic equation and anomalous Hall and spin-Hall effects

Abstract

The coupled kinetic equations for density and spin Wigner functions are derived including spinorbit coupling, electric and magnetic fields, selfconsistent Hartree meanfields 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 selfconsistent 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 consists of the known results obtained from the Kubo formula or Berry phases and a new 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.

Magnetoelectric effects in superconductors due to spin-orbit scattering: Nonlinear σ -model description

“…A nontrivial Nambu structure reflects superconducting correlations. In normal systems in the presence of spin-dependent fields [27,28], the Keldysh subblocks are 2 x 2 matrices in the spin space. G obeys the equation…”

The quantum kinetic equation and dynamical mass generation in 2+1 Dimensions

“…These above two equations Eq. (19,20) form a complete, self-consistent kinetic transport equation at zeroth order. They should be solved concurrently when solving the transport equations numerically.…”

“…Such a theory is both theoretically important as a many-body theoretical description and practically useful for describing relevant transport in a general out-of-equilibrium system. Many interesting results were obtained in 3+1 dimensions, such as the relativistic kinetic theory for scalar and fermions without external field [3], the anomalous chiral transport equation in heavy-ion collisions [4][5][6][7][8][9], the quantum kinetic theory for massive fermions under external fields [10][11][12][13][14][15][16][17][18][19], and the non-relativistic kinetic theory of spin-polarized system [20][21][22].…”