The Emergence of the Hexagonal Lattice in Two-Dimensional Wigner Fragments

TL;DR

This study uses first-principles numerical methods to demonstrate that electrons in low-density two-dimensional Wigner crystals naturally form a hexagonal lattice structure, confirming theoretical predictions.

Contribution

The paper introduces a novel numerical approach that accurately captures electron localization and crystal structure formation in 2D Wigner fragments without prior assumptions.

Findings

Hexagonal lattice structure emerges naturally in simulations.

High-spin restricted open-shell Hartree-Fock becomes exact at low density.

Method accurately captures electron localization in large systems.

Abstract

At very low density, the electrons in a uniform electron gas spontaneously break symmetry and form a crystalline lattice called a Wigner crystal. But which type of crystal will the electrons form? We report a numerical study of the density profiles of fragments of Wigner crystals from first principles. To simulate Wigner fragments we use Clifford periodic boundary conditions and a renormalized distance in the Coulomb potential. Moreover, we show that high-spin restricted open-shell Hartree-Fock theory becomes exact in the low-density limit. We are thus able to accurately capture the localisation in two-dimensional Wigner fragments with many electrons. No assumptions about the positions where the electrons will localise are made. The density profiles we obtain emerge naturally when we minimise the total energy of the system. We clearly observe the emergence of the hexagonal crystal structure which has been predicted to be ground-state structure of the two-dimensional Wigner crystal.