Nonmonotonic Temperature-Dependent Resistance in Low Density 2D Hole Gases

The low temperature longitudinal resistance-per-square $R_{\mathrm{xx}}\left(T\right)$ in ungated $\mathrm{GaAs}/{\mathrm{Al}}_x{\mathrm{Ga}}_{1-x}\mathrm{As}$ quantum wells of high peak hole mobility $1.7\times {10}^6\mathrm{cm}{}^2{\mathrm{V}}^{-1\mathrm{}}{\mathrm{s}}^{-1\mathrm{}}$ is metallic for 2D hole density $p$ as low as $3.8\times {10}^9\mathrm{cm}{}^{-2\mathrm{}}$. The electronic contribution to the resistance, $R_{\mathrm{el}}\left(T\right)$, is a nonmonotonic function of $T$, exhibiting thermal activation, $R_{\mathrm{el}}\left(T\right)\propto \exp ({-E}_a/kT)$, for $\mathrm{kT}\ll E_F$ and a heretofore unnoted decay $R_{\mathrm{el}}\left(T\right)\propto 1/T$ for $\mathrm{kT}>\mathrm{}{E}_F$. The form of $R_{\mathrm{el}}\left(T\right)$ is independent of density, indicating a fundamental relationship between the low- and high- $T$ scattering mechanisms in the metallic state.