Normal insulator → topological insulator via spin-orbit coupling
When spin-orbit coupling λ exceeds a critical value, the conduction and valence bands invert at the Γ-point. The Z₂ topological invariant changes from 0 (trivial) to 1 (topological), mandating gapless surface states by bulk-boundary correspondence. This mechanism underlies topological insulators like Bi₂Se₃.