Spin-orbit Interaction driven Topological Features in a Quantum Ring

TL;DR

This paper analytically and numerically investigates the topological and electronic properties of quantum rings with spin-orbit interactions, revealing periodic topological charge variations and magnetic field-induced currents that could be experimentally observed.

Contribution

It provides a comprehensive analysis of topological features in quantum rings with spin-orbit coupling, including the validity of models and magnetic effects, which is novel in the study of such systems.

Findings

Topological charge varies periodically with magnetic field.

Current induced by magnetic field and spin-orbit coupling is detectable.

Two-dimensional models remain reliable for large radii.

Abstract

One-dimensional quantum rings with Rashba and Dresselhaus spin-orbit couplings are studied analytically and are in perfect agreement with the numerical results. The topological charge of the spin field defined by the winding number along the ring is also studied analytically and numerically in the presence of the spin-orbit interactions. We also demonstrate the cases where the one-dimensional model is invalid for a relatively large radius. However, the numerical results of the two-dimensional model always remain reliable. Just as many physical properties of the quantum rings are influenced by the Aharonov-Bohm effect, the topological charge is also found to vary periodically due to the step-like change of the angular momentum with an increase of the magnetic field. This is significantly different from the cases of quantum dots. We also study how the current is induced by the magnetic field and spin-orbit couplings, which is strong enough that it could to be detected. The magnetic induction lines induced by the spin field and the current are also analyzed which can be observed and could perhaps help identifying the topological features of the spin fields in a quantum ring.