Topological interface modes in local resonant acoustic systems

TL;DR

This paper investigates the existence of topological interface modes in local resonant acoustic systems, revealing they only occur in band folding gaps, not in local resonant gaps, thus advancing subwavelength acoustic wave control.

Contribution

It demonstrates that topological interface states are absent in local resonant gaps but present in band folding gaps within acoustic systems, providing new insights into topological phononic design.

Findings

Topological interface states only exist in band folding gaps.

Local resonant gaps do not support topological interface modes.

Numerical results align with theoretical predictions.

Abstract

Topological phononic crystals (PCs) are periodic artificial structures which can support nontrivial acoustic topological bands, and their topological properties are linked to the existence of topological edge modes. Most previous studies focused on the topological edge modes in Bragg gaps which are induced by lattice scatterings. 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 article, we study the topological bands near local resonant gaps in a time-reversal symmetric acoustic systems and elaborate the evolution of band structure using a spring-mass model. Our acoustic structure can produce three band gaps in subwavelength region: one originates from 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. The numerical simulation perfectly agrees with theoretical results. Our study provides an approach of localizing the subwavelength acoustic wave.