Strongly Temperature-dependent Compressibility of Dilute 2D Holes near the Metal-Insulator Transition

We used the capacitance measurement to study the compressibility of dilute 2D holes in a 10nm wide GaAs quantum well for $T$=0.01-0.7K. The sample exhibits the $B$=0 metal-insulator transition (MIT) at a critical density $p_{c} \quad \sim $ 1.0 $\times $ 10$^{10 }$/cm$^{2}$. Deep in the metallic state, the sample capacitance decreases slowly as hole density $p$ increases, due to the (negative) exchange contribution to the compressibility of an interacting 2D system. As $p$ is reduced below $p_{c}$ at low-$T$, the capacitance of sample diminishes rapidly as a result of the incompressible nature of the insulator state, similar to previous studies (Dultz and Jiang, PRL 84, 4689 (2000); Allison et al., PRL 96, 216407 (2006)). On the other hand, we found that temperature has a strong effect near the MIT, in contrast to literature. In our system, the compressibility of insulator state increases with $T$ and remains positive, while the behavior of metallic phase is more complex. Notably, for metallic phase with $p$ slightly above $p_{c}$, the sign of compressibility can change from positive to negative as $T$ increases. This strongly $T$-dependent compressibility is possibly related to the competition between two phases with distinctive compressibility in our system, which is more strongly interacting than samples studied previously.