In-Gap Edge and Domain-Wall States in Largely Perturbed Phononic Su–Schrieffer–Heeger Lattices

Topological states of matter have attracted significant attention due to their intrinsic wave-guiding and localization capabilities robust against disorders and defects in electronic, photonic, and phononic systems. Despite the above topological features that phononic crystals share with their electronic and photonic counterparts, finite-frequency topological states in phononic crystals may not always survive. In this work, we discuss the survivability of topological states in Su–Schrieffer–Heeger models with both local and non-local interactions and larger symmetry perturbation. Although such a discussion is still about ideal mass-spring models, the insights from this study set the expectations for continuum phononic crystals, which can further instruct the application of phononic crystals for practical purposes.