Hole spin relaxation in Ge quantum dots

Hole spin relaxation in an isolated Ge quantum dot due to interaction with phonons is investigated. Spin relaxation in this case occurs through the mechanism of the modulation of the spin-orbit interaction by lattice vibrations. According to the calculations performed, the spin relaxation time due to direct single-phonon processes for the hole ground state equals 1.4 ms in the magnetic field H = 1 T at the temperature T = 4 K. The dependence of the relaxation time on the magnetic field is described by the power function H ⁻⁵. At higher temperatures, a substantial contribution to spin relaxation is made by two-phonon (Raman) processes. Because of this, the spin relaxation time decreases to nanoseconds as the temperature is raised to T = 20 K. Analysis of transition probabilities shows that the third and twelfth excited hole states, which are intermediate in two-step relaxation processes, play the main part in Raman processes.