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

We present calculations of the spin- and phase-relaxation rates in ${\mathrm{G}\mathrm{a}\mathrm{A}\mathrm{s}/\mathrm{A}\mathrm{l}}_{1\ensuremath{-}x}\mathrm{GaAs} p$-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 antilocalization are present due to the strong spin-orbit interaction. When determining the total conductivity correction one also has 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, ${k}_{\mathrm{B}}{T/E}_{\mathrm{F}}$ and whether the system can be considered as ballistic ${(k}_{\mathrm{B}}T{\ensuremath{\tau}}_{\mathrm{tr}}/\ensuremath{\Elzxh}g1)$ or diffusive ${(k}_{\mathrm{B}}T{\ensuremath{\tau}}_{\mathrm{tr}}/\ensuremath{\Elzxh}l1).$ 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 antilocalization 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 ${p}_{c}.$