Mesoscopic scattering dynamics under generic uniform SU(2) gauge fields: Spin-momentum relaxation and coherent backscattering

TL;DR

This paper analyzes the spin-momentum dynamics of matter waves in disordered potentials with uniform SU(2) gauge fields, providing new analytical approximations and confirming results with numerical simulations.

Contribution

It introduces an improved analytical approach for short-time spin-momentum dynamics under SU(2) gauge fields, extending beyond the diffusive approximation.

Findings

Derived the disorder-averaged density matrix as a function of time and momentum.

Presented a cubic equation for spin isotropization time with accurate asymptotic limits.

Confirmed the analytical results with numerical calculations of momentum relaxation and backscattering.

Abstract

We investigate the time- and momentum-resolved dynamics of matter waves undergoing elastic scattering from a disordered potential in the presence of spatially uniform SU(2) gauge fields. We derive the disorder-averaged density matrix as a function of time and momentum within the weak-localization regime. By accurately approximating the frequency dependence of the ladder and maximally crossed diagram series beyond the diffusive approximation, we describe short-time spin-momentum dynamics on timescales comparable to the scattering mean free time, for arbitrary strengths of the SU(2) gauge fields and disorder. We also present a cubic equation that determines the spin isotropization time, which gives accurate asymptotic forms in the limits where the spin-orbit length is much longer (Dyakonov-Perel spin relaxation regime) or much shorter than the scattering mean free path, as well as in the SU(2)-symmetric (persistent spin helix) limit. In comparison with numerical calculations, we reproduce both the relaxation of the momentum distribution and the transient backscattering peak with a momentum offset coexisting with the robust coherent backscattering dip, supporting the reliability of our calculations.