Hole spin relaxation in [001] strained asymmetric Si/SiGe and Ge/SiGe quantum wells

Abstract

Hole spin relaxation in [001] strained asymmetric $\text{Si}/{\text{Si}}_{0.7}{\text{Ge}}_{0.3}$ $(\text{Ge}/{\text{Si}}_{0.3}{\text{Ge}}_{0.7})$ quantum wells is investigated in the situation with only the lowest hole subband being relevant. The effective Hamiltonian of the lowest hole subband is obtained by the subband L\owdin perturbation method in the framework of the six-band Luttinger $\mathbf{k}\ensuremath{\cdot}\mathbf{p}$ model with sufficient basis functions included. The lowest hole subband in Si/SiGe quantum wells is light-holelike with the Rashba spin-orbit coupling term depending on momentum both linearly and cubically while that in Ge/SiGe quantum wells is a heavy-hole state with the Rashba spin-orbit coupling term depending on momentum only cubically. The hole spin relaxation is investigated by means of the fully microscopic kinetic spin Bloch equation approach with all the relevant scatterings considered. It is found that the hole-phonon scattering is very weak, which makes the hole-hole Coulomb scattering become very important. The hole system in Si/SiGe quantum wells is generally in the strong scattering limit while that in Ge/SiGe quantum wells can be in either the strong or the weak scattering limit. The Coulomb scattering leads to a peak in both the temperature- and hole-density dependences of spin relaxation time in Si/SiGe quantum wells, located around the crossover between the degenerate and nondegenerate regimes. Nevertheless, the Coulomb scattering leads to not only a peak but also a valley in the temperature dependence of spin relaxation time in Ge/SiGe quantum wells. The valley is actually due to the crossover from the weak to strong scattering limit. The hole-impurity scattering influences the spin relaxation effectively. In the strong (weak) scattering limit, the spin relaxation time increases (decreases) with increasing impurity density. The spin relaxation time is found to be on the order of $1\ensuremath{\sim}100\text{ }\text{ps}$ $(0.1\ensuremath{\sim}10\text{ }\text{ps})$ in Si/SiGe (Ge/SiGe) quantum wells, for the temperatures, carrier/impurity densities and gate voltages of our consideration.