BHZ Topological Insulator

BHZ Model (Bernevig, Hughes, Zhang 2006) describes a 2D topological insulator in HgTe quantum wells. The Hamiltonian: H(k) = ε(k)I + d(k)·σ, where d_x=Ak_x, d_y=Ak_y, d_z=M−B(k_x²+k_y²) Band inversion occurs when M/B < 0 (or more generally when the Chern number Z₂ flips). The topological invariant Z₂ = 1 (non-trivial) when |M/2B| < 1, which corresponds to band inversion at Γ. Bulk-boundary correspondence: non-trivial Z₂ → gapless helical edge states connecting valence and conduction bands. These edge states are protected from backscattering by time-reversal symmetry (spin-momentum locking).