Low density electrons crystallize when Coulomb energy ≫ kinetic energy (large r_s)
r_s = — | Phase: — | Peak S(k): —
The Wigner crystal forms when the ratio r_s = a₀/r_mean is large: Coulomb repulsion energy
E_C ~ e²/r dominates kinetic energy E_K ~ ℏ²/2mr². In 2D, crystallization occurs near r_s ≈ 37.
Electrons settle into a triangular lattice. Left: particle positions. Right: structure factor S(k)
showing Bragg peaks for crystalline order. MD simulation with Coulomb repulsion + soft confinement.