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

We reexpress the Rashba and Dresselhaus interactions as non-Abelian spin-orbit gauges and provide a perspective in understanding the persistent spin helix [B. A. Berneving , 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 nonuniform 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.