Network Model for a 2D Disordered Electron System with Spin-Orbit Scattering

TL;DR

This paper introduces a network model for 2D disordered electron systems with spin-orbit scattering, revealing a localization-delocalization transition and critical behavior through numerical analysis.

Contribution

The paper develops a novel network model for spin-orbit coupled disordered electrons and characterizes its phase transition and critical exponents.

Findings

Identifies a localization-delocalization transition in the model.

Determines the critical exponent of the localization length as approximately 2.51.

Calculates the scaling exponent of the local density of states as approximately 2.174.

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 $\nu=2.51\pm 0.18$. Based on a conformal mapping we also calculate the scaling exponent of the typical local density of states $\alpha_0=2.174 \pm 0.003$.