Hole spin relaxation in quantum dots

We present results for relaxation of the spin of a hole in a cylindrical quantum dot due to acoustic phonon assisted spin flips at low temperatures with an applied magnetic field. The hole dispersion is calculated by numerical diagonalization of the Luttinger Hamiltonian and applying perturbation theory with respect to the magnetic field, and the hole-phonon coupling is described by the Bir-Pikus Hamiltonian. We find that the decoherence time for hole spins for dots $\lesssim 20\mathrm{nm}$ is on the order of ${10}^{-8}\mathrm{s}.$ This is several orders smaller than the decoherence time due to phonon assisted processes for electron spins in similar dots and is comparable to the total decoherence time of an electron spin in a quantum dot, which is controlled by the hyperfine interaction with nuclei. We obtain the dependence of the relaxation rate of the hole spin on dot size and hole mass.