SSH Model — Topological Band Gap
The Su-Schrieffer-Heeger model is the simplest 1D topological insulator. Alternating hoppings (v, w) create a band gap. The topological phase (w > v) hosts protected edge states characterized by a winding number ν = 1.
Phase: Trivial (ν = 0)
H = Σ v·(c†_{A,n}c_{B,n}) + w·(c†_{B,n}c_{A,n+1}) + h.c. The Bloch Hamiltonian is H(k) = (v+w·cos k)σx + w·sin k·σy. Winding number ν = (1/2πi)∮(dk/dk)log det[H(k)/|H(k)|] ∈ ℤ. When w > v, ν=1 and zero-energy edge modes appear — protected by chiral symmetry even under weak disorder.