Phonon-induced decay of the electron spin in quantum dots

We study spin relaxation and decoherence in a GaAs quantum dot due to spin-orbit (SO) interaction. We derive an effective Hamiltonian which couples the electron spin to phonons or any other fluctuation of the dot potential. We show that the spin decoherence time T-2 is as large as the spin relaxation time T-1, under realistic conditions. For the Dresselhaus and Rashba SO couplings, we find that, in leading order, the effective B field can have only fluctuations transverse to the applied B field. As a result, T-2=2T(1) for arbitrarily large Zeeman splittings, in contrast to the naively expected case T-2<<T-1. We show that the spin decay is drastically suppressed for certain B-field directions and ratios of SO coupling constants. Finally, for the spin-phonon coupling, we show that T-2=2T(1) for all SO mechanisms in leading order in the electron-phonon interaction.