Metal-insulator transition in the Hartree-Fock phase diagram of the fully polarized homogeneous electron gas in two dimensions

TL;DR

This study investigates the phase diagram of a fully polarized two-dimensional electron gas using Hartree-Fock calculations, revealing a transition from a Wigner crystal to a novel charge density wave state at higher densities.

Contribution

It provides the first numerical and analytical evidence of a metal-insulator transition driven by symmetry-breaking charge density waves in the 2D electron gas.

Findings

Wigner crystal stable at low densities

Charge density wave state emerges at higher densities

Transition from insulating to conducting state identified

Abstract

We determine numerically the ground state of the two-dimensional, fully polarized electron gas within the Hartree-Fock approximation without imposing any particular symmetries on the solutions. At low electronic densities, the Wigner crystal solution is stable, but for higher densities ($r_s$ less than $\sim 2.7$) we obtain a ground state of different symmetry: the charge density forms a triangular lattice with about 11% more sites than electrons. We prove analytically that this conducting state with broken translational symmetry has lower energy than the uniform Fermi gas state in the high density region giving rise to a metal to insulator transition.