Spatial correlations in chaotic nanoscale systems with spin-orbit coupling

TL;DR

This paper studies how spin-orbit coupling affects the spatial correlations of wave functions in chaotic nanoscale systems, revealing suppression of amplitude correlations but increased importance in two-point functions, with implications for experiments.

Contribution

It provides a detailed comparison between microscopic models and random matrix theory in the context of SOC-induced crossover in eigenfunction correlations.

Findings

Wave function amplitude correlations are suppressed by SOC.

Eigenfunction correlations significantly influence two-point distribution functions.

Results have potential experimental implications.

Abstract

We investigate the statistical properties of wave functions in chaotic nanostructures with spin-orbit coupling (SOC), focussing in particular on spatial correlations of eigenfunctions. Numerical results from a microscopic model are compared with results from random matrix theory in the crossover from the gaussian orthogonal to the gaussian symplectic ensembles (with increasing SOC); one- and two-point distribution functions were computed to understand the properties of eigenfunctions in this crossover. It is found that correlations of wave function amplitudes are suppressed with SOC; nevertheless, eigenfunction correlations play a more important role in the two-point distribution function(s), compared to the case with vanishing SOC. Experimental consequences of our results are discussed.