Ground-state energy and compressibility of a disordered two-dimensional electron gas

Two-dimensional (2D) electron systems in the presence of disorder are of interest in connection with the observed metal-insulator transition in such systems. We use density functional theory in its local-spin density approximation (LSDA) to calculate the ground-state energy of a 2D electron system in the presence of remote charged impurities which up on averaging provides disorder. The inverse compressibility calculated from the ground-state energy exhibits a minimum at a critical density controlled by the disorder strength. Our findings are in agreement with experimental results.