Berry phase across the 1D Brillouin zone — topological edge states in diatomic chains
The SSH (Su-Schrieffer-Heeger) model describes a diatomic chain with alternating hoppings t₁ (intracell) and t₂ (intercell). The Zak phase γ = i∮⟨u_k|∂_k|u_k⟩dk over the Brillouin zone equals 0 or π (mod 2π). When |t₂|>|t₁|, γ=π and edge states appear at zero energy — a topological phase protected by inversion symmetry. This is a 1D analogue of the quantum Hall effect.