Rashba coupling in quantum dots: An exact solution

Abstract

We present an analytic solution to one-particle Schrödinger equation for an electron in a quantum dot with hard-wall confining potential in the presence of both magnetic field and spin-orbit coupling. Wave-functions, energy levels, and spin-flip relaxation times are calculated to all orders in the spin-orbit coupling and the magnetic field. Without the orbital contribution of the magnetic field, we find that the effective gyromagnetic ratio is strongly suppressed by the spin-orbit coupling. The spin-flip relaxation rate then has a maximum as a function of the spin-orbit coupling and is therefore suppressed in both the weak- and strong-coupling limits. In the presence of the orbital contribution of the magnetic field the effective gyromagnetic ratio changes sign in some cases.