Wigner Crystal — Low-Density 2DEG
Coulomb-driven crystallization of electrons in 2D at low rs parameter
Equilibrating...
The Wigner crystal forms when Coulomb repulsion dominates kinetic energy in a 2D electron gas. The parameter r_s = a/a_B (mean spacing / Bohr radius) controls the ratio of potential to kinetic energy. At large r_s electrons localize into a triangular (hexagonal) lattice. Monte Carlo sampling with Coulomb interactions shows the liquid-to-crystal transition near r_s ≈ 37 in 2D. Blue bonds indicate nearest-neighbor crystalline order.