Wigner Crystal Melting: 2D Electrons

At low density (high rₛ), electrons freeze into a triangular Wigner crystal due to Coulomb repulsion. The Lindemann criterion and KTHNY theory describe the melting via two continuous transitions: solid → hexatic → liquid.

Parameters

Phase

Lindemann ratio u/a
ψ₆ order param
Melt rₛ ≈37

About

Wigner (1934): electrons crystallize when potential energy ≫ kinetic energy, i.e. rₛ ≫ 1. In 2D, Tanatar-Ceperley (1989) QMC: rₛ_c ≈ 37. KTHNY theory (Kosterlitz-Thouless-Halperin-Nelson-Young): two transitions mediated by dislocation and disclination unbinding. Lindemann: melts when u/a ≈ 0.1.