Spin relaxation and anticrossing in quantum dots: Rashba versus Dresselhaus spin-orbit coupling

The spin-orbit splitting of the electron levels in a two-dimensional quantum dot in a perpendicular magnetic field is studied. It is shown that at the point of an accidental degeneracy of the two lowest levels above the ground state the Rashba spin-orbit coupling leads to a level anticrossing and to mixing of spin-up and spin-down states, whereas there is no mixing of these levels due to the Dresselhaus term. We calculate the relaxation and decoherence times of the three lowest levels due to phonons. We find that the spin relaxation rate as a function of a magnetic field exhibits a cusplike structure for Rashba but not for Dresselhaus spin-orbit interaction.

Figure 1

(Color online). Contributions to the relaxation rate $1∕T_1$ of phonon-induced transitions between the states $\mid 1⟩$, $\mid 2⟩$, and $\mid 3⟩$ of a GaAs QD with $\hslash {\omega }_0=1.1\mathrm{meV}$ and $d=5\mathrm{nm}$ due to (a) the Dresselhaus and (b) the Rashba SO couplings $({\lambda }_D={\lambda }_R=8\mu \mathrm{m})$. The dashed and dot-dashed curves are orbital relaxation rates, the solid and dotted curves are the relaxation rates with a spin flip. The crossing (a) and the anticrossing (b) of the levels $E_3$ and $E_2$ are shown in the insets. The cusplike structure of the spin relaxation curve due to the Rashba SO coupling is caused by the mixing of the spin-up and spin-down states at the anticrossing.