Spin relaxation in quantum dots with random spin-orbit coupling

We investigate the longitudinal spin relaxation arising due to spin-flip transitions accompanied by phonon emission in quantum dots where the strength of the Rashba spin-orbit coupling is a random function of the lateral (in-plane) coordinate on the spatial nanoscale. In this case the Rashba contribution to the spin-orbit coupling cannot be completely removed by applying a uniform external bias across the quantum dot plane. Due to the remnant random contribution, the spin relaxation rate cannot be decreased by more than two orders of magnitude even when the external bias fully compensates the regular part of the spin-orbit coupling.