Ground-state energy and Wigner crystallization in thick 2D-electron systems

TL;DR

This paper investigates the ground-state energy and Wigner crystallization in thick 2D electron systems, comparing theoretical approximations with quantum Monte Carlo results to understand phase transitions in these materials.

Contribution

It introduces and compares LDA and CDA methods for evaluating exchange-correlation energy in thick 2D electron layers, extending understanding of Wigner crystallization.

Findings

LDA and CDA estimates for Wigner transition in perfect 2D fluid are at $r_s=38$ and 32.

For thick 2D layers, Wigner transition predicted at $r_s=20.5$ and 15.5.

LDA and CDA predictions align reasonably with quantum Monte Carlo results.

Abstract

The ground state energy of the 2-D 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 $r_s=35\pm5$ 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.