Spin-orbit interaction and the 'metal-insulator' transition observed in two-dimensional hole systems

Abstract

We present calculations of the spin and phase relaxation rates in GaAs/AlGaAs $p$-type quantum wells. These rates are used to derive the temperature dependence of the weak-localization correction to the conductivity. In $p$-type quantum wells both weak localization and weak anti-localization are present due to the strong spin-orbit interaction. When determining the total conductivity correction one also have to include the term due to hole-hole interaction. The magnitude of the latter depends on the ratio between the thermal energy and the Fermi energy, $k_{\rm B}T/E_{\rm F}$ and whether the system can be considered as ballistic $(k_{\rm B}T τ_{\rm tr} / \hbar>1)$ or diffusive ($k_{\rm B}T τ_{\rm tr}/\hbar<1$). We argue that due to the relatively low Fermi energy and the moderate mobilities, in the $p$-type systems in question, the conductivity correction arising from hole-hole interactions is negligible at the highest temperatures accessible in the experiments. Hence the 'metal-insulator' transition observed at these relatively high temperatures could be caused by interference effects. We compare our calculations of the weak anti-localization correction with the experimental results from different independent groups with special emphasis on the experiments by Simmons et al. We find good agreement between predicted and observed transistion density $p_{c}$.