Wigner Crystal (1934)
At sufficiently low density (high r_s = a_0/a, where a is mean electron spacing), the kinetic energy is small compared to Coulomb repulsion, and electrons crystallize into a triangular lattice — the Wigner crystal.
The Wigner-Seitz parameter r_s = 1/(√π n a_0) (2D) controls the phase: for r_s ≳ 37 (2D), the electron liquid freezes. Experimentally observed in 2D electron gases on liquid helium (Grimes & Adams, 1979).
The hexagonal bond-orientation order parameter ψ₆ = |⟨e^{i6θ}⟩| distinguishes crystal (ψ₆→1) from liquid (ψ₆→0). This simulation uses Langevin molecular dynamics with Ewald-like 1/r repulsion.
Wigner crystal
2D electron gas
Coulomb crystallization
KTHNY melting