Degenerate versus semi-degenerate transport in a correlated 2D hole system

It has been puzzling that the resistivity of high mobility two-dimensional(2D) carrier systems in semiconductors with low carrier density often exhibits a large increase followed by a decrease when the temperature ($T$) is raised above a characteristic temperature comparable with the Fermi temperature ($T_F$). We find that the metallic 2D hole system (2DHS) in GaAs quantum well (QW) has a linear density ($p$) dependent conductivity, $\sigma\approx e\mu^*(p-p_0)$, in both the degenerate (T<<T_F) and semi-degenerate (T T_F) regimes. The $T$-dependence of $\sigma(p)$ suggests that the metallic conduction (d$\sigma$/d$T<$0) at low $T$ is associated with the increase in $\mu^*$, the effective mobility of itinerant carriers. However, the resistivity decrease in the semi-degenerate regime ($T>T_F$) is originated from the reduced $p_0$, the density of immobile carriers in a two-phase picture.