Semiclassical theory of diffusive-ballistic crossover and the persistent spin helix

Conventional transport theory focuses on either the diffusive or ballistic regimes and neglects the crossover region between the two. In the presence of spin-orbit coupling, the transport equations are known only in the diffusive regime, where the spin precession angle is small. In this paper, we develop a semiclassical theory of transport valid throughout the diffusive-ballistic crossover of a special SU(2) symmetric spin-orbit-coupled system. The theory is also valid in the physically interesting regime where the spin precession angle is large. We obtain exact expressions for the density and spin structure factors in both two-dimensional and three-dimensional samples with spin-orbit coupling.