Narrow quantum rings with general Rashba and Dresselhaus spin-orbit interactions

Abstract

We solve the energy eigenvalue problem of narrow semiconductor quantum rings including the Rashba and Dresselhaus spin-orbit interactions with general coupling constants. We show that the eigenstates of the system can be expressed as products of a scalar Mathieu function and a spinor function which is either periodic or pseudo-periodic on the ring coordinate. The spinor functions are solutions to an ordinary differential equation on the ring coordinate which is analogous to the time-dependent Schrödinger equation. The eigenenergies of the ring correspond to the eigenvalues of the Mathieu function. For realistic material parameters, satisfactory analytical solutions can be obtained using standard approximations. Our solution method can be applied to quantum rings with a general linear-in-k spin-orbit interactions.