Berry curvature Ω(k) = -2 Im ⟨∂_kx u|∂_ky u⟩ acts as a magnetic field in momentum space. For a two-band model H(k) = d(k)·σ, the curvature is Ω(k) = -½ d̂·(∂_kx d̂ × ∂_ky d̂), measuring how the pseudo-spin winds around the Brillouin zone. The Chern number C = (1/2π)∫ Ω(k) d²k is always an integer, counting monopole charge at band-touching points. When |m| < 2t (here m/gap ≠ 0), the Dirac point shifts and topological phase transitions occur — the Chern number changes by ±1 each time a Dirac cone passes through k=0.