Spin relaxation in lateral quantum dots: Effects of spin-orbit interaction

We report results of calculations of the effect of spin-orbit interaction on electron spin relaxation in a lateral quantum dot. Our study is motivated by puzzling results of high source-drain transport measurements of singlet-triplet transitions of two electrons in lateral and vertical devices that show a strong asymmetry as a function of the applied magnetic field. Using exact diagonalization techniques, we investigate the influence of the spin-orbit interaction on the energy levels of a two-electron droplet and we show that the spin-orbit interaction strongly affects the expectation values of the total and z-projection spins of the two-electron system. We then evaluate the energy relaxation rates for the two-electron droplet through the emission of longitudinal acoustic phonons and show that they are strongly dependent on the spin energy levels involved in the process. Our study shows that the spin-orbit interaction provides an effective coupling between the spin-polarized triplet states and the singlet state. However, the transition involving the spin singlet and the unpolarized triplet component is very weak even in the presence of spin-orbit interaction. The calculated scattering rates from the excited states to the ground state of the two-electron system clearly confirm this picture and reveal a microsecond time scale for the single-triplet relaxation through spin-orbit-mediated acoustic phonon emission and the relaxation mechanism presents a built-in magnetic field asymmetry, in qualitative agreement with experimental findings.