Critical Quantum Chaos in 2D Disordered Systems with Spin-Orbit Coupling

TL;DR

This paper investigates the applicability of semi-Poisson level spacing distribution as a signature of critical quantum chaos in 2D disordered systems with spin-orbit coupling, especially at the Anderson transition.

Contribution

It demonstrates that semi-Poisson distribution accurately describes critical level statistics in 2D disordered systems with spin-orbit coupling at the Anderson transition.

Findings

Semi-Poisson distribution fits the critical level spacing at the Anderson transition.

The number variance shows a linear behavior with a specific asymptotic value.

Critical statistics are intermediate between Wigner and Poisson distributions.

Abstract

We examine the validity of the recently proposed semi-Poisson level spacing distribution function P(S), which characterizes `critical quantum chaos', in 2D disordered systems with spin-orbit coupling. At the Anderson transition we show that the semi-Poisson P(S) can describe closely the critical distribution obtained with averaged boundary conditions, over Dirichlet in one direction with periodic in the other and Dirichlet in both directions. We also obtain a sub-Poisson linear number variance $\Sigma_{2}(E)\approx \chi_{0}+ \chi E$, with asymptotic value $\chi\approx0.07$. The obtained critical statistics, intermediate between Wigner and Poisson, is relevant for disordered systems and chaotic models.