Spin relaxation rates in quasi-one-dimensional coupled quantum dots

We study theoretically the electron-spin relaxation rate in quasi-one-dimensional coupled semiconductor quantum dots. The cross-sectional confinement or shape of these nanorods can be chosen so that either the Rashba or the Dresselhaus spin-orbit coupling is present. We consider acoustic-phonon-mediated transitions between the ground state and the next two higher-energy eigenstates. These three states are nondegenerate due to the interdot coupling, which causes a symmetric-antisymmetric gap, and a competition with the Zeeman splitting. With Rashba coupling and at fixed Zeeman splitting the two upper states display an anticrossing versus interdot barrier width, which is shown to be associated with a sharp cusp in the spin relaxation rate.