Random matrix theory for closed quantum dots with weak spin-orbit coupling

TL;DR

This paper applies random matrix theory to analyze how weak spin-orbit coupling affects the electronic properties of quantum dots, revealing significant changes in Coulomb blockade peak distributions and potentially explaining experimental discrepancies.

Contribution

It introduces a spin-dependent flux model that decouples spin ensembles, providing new insights into the impact of spin-orbit coupling on quantum dot statistics.

Findings

Decrease in the width of Coulomb blockade peak height distribution

Significant changes in the distribution due to spin-orbit effects

Potential explanation for experimental discrepancies

Abstract

To lowest order in the coupling strength, the spin-orbit coupling in quantum dots results in a spin-dependent Aharonov-Bohm flux. This flux decouples the spin-up and -down random matrix theory ensembles of the quantum dot. We employ this ensemble and find significant changes in the distribution of the Coulomb blockade peak height, in particular a decrease of the width of the distribution. The puzzling disagreement between standard random matrix theory and the experimental distributions by Patel et al. might possibly be attributed to these spin-orbit effects.