1D dimerized chain with alternating spring constants — topological edge modes in the bandgap
The Su-Schrieffer-Heeger (SSH) model for phonons: a 1D chain with alternating spring constants k₁=k(1+δ) and k₂=k(1−δ). Bands: ω²(q) = k[1 ± √(1+δ²+2δcos(qa))], with a bandgap for δ≠0. For δ>0 the chain is topologically nontrivial (Zak phase = π) and hosts exponentially localized edge modes inside the gap — mechanical analogs of topological insulators.