U/t ratio:
4.00
H = -t Σ c†ᵢσcⱼσ + U Σ nᵢ↑nᵢ↓ - μ Σ nᵢ
t = hopping amplitude
U = on-site repulsion
μ = chemical potential
Half-filling (n=1):
• U/t ≪ 1 → metal
• U/t ≫ 1 → Mott insulator
(one electron per site,
motion frozen by cost U)
Mott transition: at U/t ≈ 8–12, double occupancy becomes too costly → electrons localize despite partial band filling. NOT a band insulator.
d-wave SC: doping the Mott insulator (n≠1) produces high-Tc superconductivity — the mechanism behind cuprate superconductors.