Two-band model H(k) = d(k)·σ. Tuning a parameter drives gap closing at a time-reversal-invariant momentum, signaling a topological phase transition (Z₂ invariant change).
Topological phase (ν = 1)
Model: H(k) = sin(k)σₓ + (M + cos(k))σ_z (SSH-like / BHZ). Band gap closes at k=0 when M=−1 and k=π when M=+1. Topological invariant: winding number ν = sign changes of d_z(k) / 2. Edge states appear inside the gap in topological phase.