Network model for a two-dimensional disordered electron system with spin-orbit scattering

Abstract

We introduce a network model to describe two-dimensional disordered electron systems with spin-orbit scattering. The network model is defined by a discrete unitary time-evolution operator. We establish by numerical transfer matrix calculations that the model exhibits a localization-delocalization transition. We determine the corresponding phase diagram in the parameter space of disorder scattering strength and spin-orbit scattering strength. Near the critical point we determine by statistical analysis a one-parameter scaling function and the critical exponent of the localization length to be $\nu =2.51\mathrm{}\pm \mathrm{0.18.}$ Based on a conformal mapping we also calculate the scaling exponent of the typical local density of states ${\alpha }_0=2.174\mathrm{}\pm \mathrm{0.003.}$