Non-Abelian spin-orbit gauge: Persistent spin helix and quantum square ring

TL;DR

This paper reformulates Rashba and Dresselhaus spin-orbit interactions as non-Abelian gauge fields, offering new insights into persistent spin helix phenomena and analyzing quantum square rings with diverse spin states.

Contribution

It introduces a gauge-theoretic framework for spin-orbit interactions and develops a general tight-binding Hamiltonian for non-uniform systems, applying it to quantum ring devices.

Findings

Reexpression of spin-orbit interactions as non-Abelian gauges.

Transformation of certain models into free electron gases.

Identification of four distinct states in quantum square rings.

Abstract

We re-express the Rashba and Dresselhaus interactions as non-Abelian spin-orbit gauges and provide a new perspective in understanding the persistent spin helix [Phys. Rev. Lett. 97, 236601 (2006)]. A spin-orbit interacting system can be transformed into a free electron gas in the equal-strength Rashba-Dresselhaus [001] linear model, the Dresselhaus [110] linear model, and a one-dimensional system. A general tight-binding Hamiltonian for non-uniform spin-orbit interactions and hoppings along arbitrary directions, within the framework of finite difference method, is obtained. As an application based on this Hamiltonian, a quantum square ring in contact with two ideal leads is found to exhibit four states, insulating, spin-filtering, spin-flipping, and spin-keeping states.