EFFECTS OF SPIN-ORBIT INTERACTIONS IN DISORDERED CONDUCTORS - A RANDOM-MATRIX APPROACH

A description in terms of random matrices is used to study the effects of strong spin-orbit coupling in disordered conductors. It is shown that the ensemble of transfer matrices can be conveniently parametrized using quaternions. A diffusion equation is derived for the evolution, with sample length, of the transfer-matrix distribution. In the insulating regime, a uniform density of Lyapunov exponents is obtained, and the expected universal multiplication factors in the localization length are derived when time-reversal symmetry is broken. Weak antilocalization, backscattering depletion, and universal conductance fluctuations are obtained in the metallic regime.