Topological phononic crystals (PCs) are periodic artificial structures whichcan support nontrivial acoustic topological bands, and their topologicalproperties are linked to the existence of topological edge modes. Most previousstudies focused on the topological edge modes in Bragg gaps which are inducedby lattice scatterings. While local resonant gaps would be of great use insubwavelength control of acoustic waves, whether it is possible to achievetopological interface states in local resonant gaps is a question. In thisarticle, we study the topological bands near local resonant gaps in atime-reversal symmetric acoustic systems and elaborate the evolution of bandstructure using a spring-mass model. Our acoustic structure can produce threeband gaps in subwavelength region: one originates from local resonance of unitcell and the other two stem from band folding. It is found that the topologicalinterface states can only exist in the band folding induced band gaps but neverappear in the local resonant band gap. The numerical simulation perfectlyagrees with theoretical results. Our study provides an approach of localizingthe subwavelength acoustic wave.
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