Kinetic theory of spin-polarized systems in electric and magnetic fields with spin-orbit coupling. II. RPA response functions and collective modes

Abstract

The spin and density response functions in the random phase approximation (RPA) are derived by linearizing the kinetic equation including a magnetic field, the spin-orbit coupling, and mean fields with respect to an external electric field. Different polarization functions appear describing various precession motions showing Rabi satellites due to an effective Zeeman field. The latter turns out to consist of the mean-field magnetization, the magnetic field, and the spin-orbit vector. The collective modes for charged and neutral systems are derived and a threefold splitting of the spin waves dependent on the polarization and spin-orbit coupling is shown. The dielectric function including spin-orbit coupling, polarization and magnetic fields is presented analytically for long wave lengths and in the static limit. The dynamical screening length as well as the long-wavelength dielectric function shows an instability in charge modes, which are interpreted as spin segregation and domain formation. The spin response describes a crossover from damped oscillatory behavior to exponentially damped behavior dependent on the polarization and collision frequency. The magnetic field causes ellipsoidal trajectories of the spin response to an external electric field and the spin-orbit coupling causes a rotation of the spin axes. The spin-dephasing times are extracted and discussed in dependence on the polarization, magnetic field, spin-orbit coupling and single-particle relaxation times.

Dynamical charge and pseudospin currents in graphene and possible Cooper pair formation

“…The dynamical result is given by the frequency dependence (45) in (66) and (65). We see that the anomalous Hall effect vanishes with vanishing effective Zeeman field (34).…”

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

“…Next, we move on to discuss the transport equation for f (1) (x, p), which is determined by the second equation of Eq. (21). Substituting the solution for V µ…”

“…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].…”

Weyl systems: anomalous transport normally explained

“…Though it has been shown that (22) provide anomalous Hall conductivity 97 , spin-density waves 103 and graphene transport 99 directly, it is now useful to map this equation system to the helicity basis used in the literature. This will enlighten the connection to anomalous transport with Berry curvatures.…”

“…In this way we concentrate only on the linear electric field response since we are searching for E • B terms. The complete response functions are given in 103 . The advantage of writing the linearization in the two-step form (85) and ( 84) is that the scalar density response becomes…”