Metal-insulator transition in the two-dimensional fully polarized homogeneous electron gas from Hartree-Fock solutions

TL;DR

This paper investigates the metal-insulator transition in a two-dimensional fully polarized electron gas using Hartree-Fock solutions, revealing a transition from a Wigner crystal to a symmetry-broken conducting state at higher densities.

Contribution

It provides a detailed Hartree-Fock analysis of the ground state without symmetry constraints, identifying a novel conducting phase with broken translational symmetry.

Findings

Wigner crystal is stable at low densities

A new conducting state emerges at higher densities

Transition from insulator to metal occurs around r_s ~ 3

Abstract

We determine 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 $\sim 3$) we obtain a ground state of different symmetry: the charge density forms a triangular lattice with about 11% more sites than electrons. We argue that this conducting state with broken translational symmetry remains the ground state of the high density region in the thermodynamic limit giving rise to a metal to insulator transition.