Spin relaxation in quantum dots

Abstract

Results are given for spin relaxation in quantum dots due to acoustic phonon-assisted flips of single spins at low temperatures. The dominant spin relaxation processes for varying dot size, temperature, and magnetic field are identified. These processes are mediated by the spin-orbit interaction and are described within a generalized effective mass treatment. Particular attention is given to phonon coupling due to interface motion, which dominates the relaxation for dots with diameters $\lesssim 15\mathrm{nm},$ and also to a direct spin-phonon process that arises from valence-conduction band coupling and dominates the rates for increasing temperature. Low-temperature relaxation rates are found to be small and to depend strongly on size, on temperature, and on magnetic field. Results are illustrated with evaluations for $\mathrm{GaAs}/{\mathrm{Al}}_x{\mathrm{Ga}}_{1-x}\mathrm{As}$ systems, and a minimum in the relaxation rate is found for dot diameters $\sim 20\mathrm{nm}.$