Wigner Crystal — Electron Lattice Formation

Classical 2D electron lattice: Coulomb repulsion vs thermal disorder

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Wigner crystal forms when r_s = a/a_B ≫ 1 (dilute limit): electron spacing a ≫ Bohr radius a_B. Potential energy ~e²/a dominates kinetic ~ℏ²/ma². Wigner (1934): triangular lattice minimizes energy. Quantum melting at r_s ≈ 37 (2D), classical melting via KTHNY theory (Kosterlitz-Thouless-Halperin-Nelson-Young).