SSH Model

Su-Schrieffer-Heeger chain — paradigmatic 1D topological insulator with chiral symmetry




TOPOLOGICAL (w=1)

Bulk Band Structure E(k)

Winding Number & Bloch Vector

Open Chain Spectrum

Edge State Wavefunction

SSH Model (Su, Schrieffer, Heeger 1979) describes polyacetylene: alternating hoppings v (intracell) and w (intercell). Bulk Hamiltonian: H(k) = (v+w·cosk)σₓ + (w·sink)σᵧ. The winding number ν = (1/2π)∮ dφ(k) counts how many times the Bloch vector winds around the origin as k traverses the BZ. ν=0 (trivial, v>w); ν=1 (topological, v<w). Bulk-boundary correspondence: ν=1 → 2 zero-energy edge states, exponentially localized with decay length ξ = 1/log(w/v). Protected by chiral symmetry Γ: {H,Γ}=0.