Chaotic transport in the symmetry crossover regime with a spin-orbit interaction

We study a chaotic quantum transport in the presence of a weak spin-orbit interaction. Our theory covers the whole symmetry crossover regime between time-reversal invariant systems with and without a spin-orbit interaction. This situation is experimentally realizable when the spin-orbit interaction is controlled in a conductor by applying an electric field. We utilize a semiclassical approach which has recently been developed. In this approach, the non-Abelian nature of the spin diffusion along a classical trajectory plays a crucial role. New analytical expressions with one crossover parameter are semiclassically derived for the average conductance, conductance variance, and shot noise. Moreover numerical results on a random-matrix model describing the crossover from the Gaussian orthogonal ensemble to the Gaussian symplectic ensemble are compared with the semiclassical expressions.