Time evolution of coherent wave propagation and spin relaxation in spin-orbit-coupled systems

We investigate, both numerically and analytically, the time evolution of a particle in an initial plane-wave state as it is subject to elastic scattering in a two-dimensional disordered system with Rashba spin-orbit coupling (SOC). In the analytic calculation, we treat the SOC nonperturbatively and the disorder perturbatively using the diffuson and the cooperon. We calculate the time dependence of coherent backscattering as a function of the strength of the SOC. We identify weak and strong SOC regimes and give the relevant time and energy scales in each case. By studying the time dependence of the anisotropy of the disorder-averaged momentum distribution, we identify the spin-relaxation time. We find a crossover from D'yakonov-Perel' spin relaxation for weak SOC to Elliot-Yafet-like behavior for strong SOC.