Spin–orbit interaction and spin relaxation in a lateral quantum dot

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 transition of two electrons in lateral and vertical devices that show a strong asymmetry as a function of the applied magnetic field. On the low magnetic field side of the singlet–triplet transition, both the singlet ground state and the excited triplet state are experimentally resolved. Once the triplet becomes ground state, the singlet excited state is no longer observed. By exact diagonalization techniques, we evaluate the energy levels of a two-electron droplet in the presence of both Dresselhaus and Rashba contributions to the spin–orbit interaction. We then evaluate the energy relaxation rates for the two-electron droplet through the emission of LA phonons and show that they are strongly dependent on the spin of the energy levels involved in the process: transitions involving spin singlet and unpolarized triplet states remain forbidden even in the presence of spin–orbit interaction. This dephasing mechanism presents a built-in magnetic field asymmetry in qualitative agreement with experimental findings.