Berry curvature in Brillouin zone → σ_xy = (e²/h) × C (TKNN)
Chern number C = 1 | σ_xy = 1 × e²/h
The TKNN formula (Thouless, Kohmoto, Nightingale, den Nijs 1982) shows that the Hall conductance of a filled Landau level is quantized as σ_xy = Ce²/h, where C is the first Chern number — an integer topological invariant equal to the Berry flux integrated over the Brillouin zone. Edge states carry the current, immune to disorder.