Relaxation times of the two-phonon processes with spin-flip and spin-conserving in quantum dots

We perform a theoretical investigation on the two-phonon processes of the spin-flip and spin-conserving relaxation in quantum dots in the frame of the Huang-Rhys' lattice relaxation model. We find that the relaxation time of the spin-flip is two orders of magnitude longer than that of the spin-conserving, which is in agreement with previous experimental measurements. Moreover, the opposite variational trends of the relaxation time as a function of the energy separation for two-phonon processes are obtained in different temperature regime. The relaxation times display the oscillatory behaviors at the demarcation point with increasing magnetic field, where the energy separation matches the optical phonon energy and results in the optical phonon resonance. These results are useful in understanding the intraband levels' relaxation in quantum dots and could be helpful in designing photoelectric and spin-memory devices