Topological interface modes in local resonant acoustic systems

Topological phononic crystals are artificial periodic structures that can support nontrivial acoustic topological bands, and their topological properties are linked to the existence of topological edge modes. Most previous studies have been focused on the topological edge modes in Bragg gaps, which are induced by lattice scattering. While local resonant gaps would be of great use in subwavelength control of acoustic waves, whether it is possible to achieve topological interface states in local resonant gaps is a question. In this paper, we study the topological properties of subwavelength bands in a local resonant acoustic system and elaborate the band-structure evolution using a spring-mass model. Our acoustic structure can produce three band gaps in the subwavelength region: one originates from the local resonance of unit cell and the other two stem from band folding. It is found that the topological interface states can only exist in the band-folding-induced band gaps, but never appear in the local resonant band gap. In addition, the numerical simulation in a practical system perfectly agrees with the theoretical results. Our study provides an effective approach of producing robust acoustic topological interface states in the subwavelength region.