Ground-state energy and Wigner crystallization in thick two-dimensional electron systems

Abstract

The ground-state energy of the two-dimensional (2D) Wigner crystal is determined as a function of the thickness of the electron layer and the crystal structure. The method of evaluating the exchange-correlation energy is tested using known results for the infinitely thin 2D system. Two methods, one based on the local-density approximation (LDA), and another based on the constant-density approximation (CDA) are established by comparing with quantum Monte Carlo (QMC) results. The LDA and CDA estimates for the Wigner transition of the perfect 2D fluid are at ${r}_{s}=38$ and 32, respectively, compared with ${r}_{s}=35\ifmmode\pm\else\textpm\fi{}5$ from QMC. For thick-2D layers as found in Hetero-junction-insulated-gate field-effect transistors, the LDA and CDA predictions of the Wigner transition are at ${r}_{s}=20.5$ and 15.5, respectively. Impurity effects are not considered here.