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, \textit{$\sigma \approx $e$\mu $}$^{\ast }(p-p_{0})$, in both the degenerate ($T <T_{F})$ is originated from the reduced $p_{0}$, the density of immobile carriers in a two-phase picture. Quantum oscillations in the magneto-resistivity are also found to persist into the semi-degenerate regime in our strongly correlated 2DHS.