Chern insulators have a quantized Hall conductance σ_xy = Ce²/h where C is the Chern number. The bulk-edge correspondence guarantees |C| topologically protected edge modes crossing the gap — spectral flow as flux is threaded.
Qi-Wu-Zhang (2006): H(k)=sin(kx)σx+sin(ky)σy+(m+cos(kx)+cos(ky))σz. C=0 for |m|>2, C=±1 for 0<|m|<2, C=0 for m=0 (critical). Spectral flow: threading flux Φ through a cylinder shifts edge mode energies — each gap crossing counts +1 toward the Chern number.