Spin relaxation in quantum dots

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 less than or similar to15 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 GaAs/AlxGa1-xAs systems, and a minimum in the relaxation rate is found for dot diameters similar to20 nm.