Berry curvature:
Ω_n(k) = −2 Im Σ_{m≠n} <n|∂_kx H|m><m|∂_ky H|n>/(E_m−E_n)²
Chern number:
C = (1/2π)∫∫_BZ Ω(k) d²k
Hall conductivity:
σ_xy = C·e²/h
Haldane model: graphene + NNN hopping + flux. Color: +Ω (red/hot) → −Ω (blue/cool)