Non-Abelian Geometric Phases and Conductance of Spin-3/2 Holes

TL;DR

This paper explores how spin-3/2 holes in semiconductors acquire nonabelian geometric phases during motion, affecting conductance oscillations, with a focus on ring and figure-8 geometries.

Contribution

It introduces a general framework for analyzing nonabelian geometric phases in spin-3/2 holes and computes conductance effects in specific geometries.

Findings

Conductance oscillations are influenced by nonabelian geometric phases.

Nonabelian interference effects are significant in figure-8 geometries.

A new theoretical framework for analyzing spin-3/2 hole systems is proposed.

Abstract

Angular momentum $J=3/2$ holes in semiconductor heterostructures are showed to accumulate nonabelian geometric phases as a consequence of their motion. We provide a general framework for analyzing such a system and compute conductance oscillations for a simple ring geometry. We also analyze a figure-8 geometry which captures intrinsically nonabelian interference effects.