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

Area of Science:

• Condensed matter physics
• Quantum mechanics
• Materials science

Background:

• Electrons in a uniform electron gas can spontaneously form a Wigner crystal at very low densities.
• The specific crystal structure adopted by Wigner crystals is a key question in condensed matter physics.
• Understanding Wigner crystal formation is crucial for developing novel electronic materials.

Purpose of the Study:

• To numerically investigate the density profiles of Wigner crystal fragments from first principles.
• To determine the ground-state crystal structure of two-dimensional Wigner crystals.
• To validate theoretical predictions regarding electron localization and crystal formation.

Main Methods:

• Simulation of Wigner fragments using Clifford periodic boundary conditions.
• Application of a renormalized distance in the Coulomb potential for accurate electron-electron interactions.
• Utilizing high-spin restricted open-shell Hartree-Fock theory, which becomes exact in the low-density limit.

Main Results:

• Accurate capture of electron localization in two-dimensional Wigner fragments with numerous electrons.
• Density profiles emerged naturally from energy minimization without prior assumptions on electron positions.
• Clear observation of the emergence of the hexagonal crystal structure.

Conclusions:

• The hexagonal crystal structure is confirmed as the ground state for two-dimensional Wigner crystals.
• First-principles numerical studies provide robust evidence for predicted Wigner crystal structures.
• The employed methods accurately model electron behavior in low-density quantum systems.