Two-phonon process and hyperfine interaction limiting slow hole-spin relaxation time in InAs/GaAs quantum dots

We study the hole-spin relaxation in p-doped InAs quantum dots. Two relaxation mechanisms are evidenced, at low magnetic field ($0\ensuremath{\le}B\ensuremath{\le}2T$) and low temperature ($2\ensuremath{\le}T\ensuremath{\le}50K$), by using a pump-probe configuration and a recent experimental technique working in the frequency domain. At $T=2K$, the coupling to nuclear spins and the hole wave-function inhomogeneity fix the hole-spin relaxation rate value, ${\ensuremath{\Gamma}}_{1}^{h}\ensuremath{\approx}1\phantom{\rule{0.28em}{0ex}}\ensuremath{\mu}{\mathrm{s}}^{\ensuremath{-}1}$. It decreases with increasing magnetic field and reaches a plateau at 0.4 $\ensuremath{\mu}{\mathrm{s}}^{\ensuremath{-}1}$. At $T\ensuremath{\ge}7K$, two-phonon spin-orbit process dominates and leads to a quadratic temperature dependence of ${\ensuremath{\Gamma}}_{1}^{h}$, in good agreement with theory.