Topological Winding Number

H(k) traces a loop in parameter space; winding around origin = topological invariant

Intra-cell hopping t: 1.00 Inter-cell hopping t': 0.40

W = 1 (Topological)

SSH H(k) = (t+t'cosk)σ_x + t'sink σ_y
W = winding of H(k) around origin
t' < t → W=1, edge states exist
t' > t → W=0, trivial bulk
Bulk-boundary correspondence:
W edge states = W zero modes

Topological Winding Number — SSH Model