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

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