Level statistics in a two-dimensional system with strong spin-orbit coupling

TL;DR

This paper investigates the spectral statistics of a two-dimensional system with strong spin-orbit coupling, revealing that large splitting leads to orthogonal ensemble behavior, contrary to common expectations, with a resonance at the SO splitting energy.

Contribution

It demonstrates that strong spin-orbit coupling can result in orthogonal ensemble statistics, challenging the typical association with symplectic statistics in such systems.

Findings

Level correlations follow orthogonal Wigner-Dyson statistics at large SO splitting.

Level statistics are governed by transitions between split spectrum branches.

A resonance occurs at the energy equal to the SO splitting.

Abstract

We study level correlations in a two-dimensional system with a long-range random potential and strong spin-orbit (SO) splitting of the spectrum. The level correlations for sufficiently large splitting are shown to be described by orthogonal Wigner-Dyson statistics, in contrast to the common point of view that a system with the strong SO coupling belongs to the symplectic statistical ensemble. We demonstrate also that in a wide energy interval the level statistics is completely determined by transitions between two branches of the split spectrum. A sharp resonance is obtained in the two-level correlation function at energy equal to the value of SO splitting.