Wigner Crystal: Coulomb Electron Ordering

Crystallization of electrons at low density via Coulomb repulsion

Wigner Crystal

Electrons in a uniform positive background (jellium model) form a crystal when Coulomb energy dominates kinetic energy — parameterized by r_s, the Wigner-Seitz radius.

r_s = (3/4πn)^(1/3) / a_B (mean inter-electron spacing) E/N = 2.21/r_s² - 0.916/r_s (kinetic - exchange) + correlation terms Wigner crystal forms: r_s ≳ 106 (Ceperley-Alder, QMC 1980) Ground state: triangular lattice Phonon modes: acoustic + optical ω_p = √(4πne²/m) (plasma freq)

The Wigner crystal was predicted in 1934 — first observed experimentally on liquid helium surface (1979), and in 2D electron gases in GaAs/AlGaAs heterostructures.

Computing...