Berry curvature acts as a momentum-space magnetic field — its integral over occupied bands gives the intrinsic Hall conductivity
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σ_xy = (e²/ℏ) ∫_BZ Ω_n(k) d²k/(2π)² — Berry curvature Ω = ∇_k × A_k accumulates at anticrossings and monopoles in k-space, driving transverse Hall current without B field.