Theory of spin-orbit effects and spin relaxation in single and coupled quantum dots.

Spin-orbit effects and phonon-induced spin relaxation in laterally coupled quantum dots in the presence of magnetic field are investigated by exact numerical diagonalization. Both Bychkov-Rashba and Dresselhaus spin-orbit couplings are included. Several new phenomena are predicted. In particular, we shown that coherent tunneling between the dots depend on the spin, enabling a scheme for spin-to-charge conversion by spin separation in a {\it homogeneous} magnetic field. Furthermore, we show that spin relaxation is highly anisotropic, both in terms of the direction of the double-dot axis as well as the direction of the magnetic field. The anisotropy comes from spin-orbit coupling. Calculated spin relaxation rates of GaAs single dots agree with a recent experiment.