Bragg scattering based acoustic topological transition controlled by local resonance

Topological metamaterials offer new routes for control of waves, which are widely realized by Bragg scattering and/or local resonance. Understanding of topological transition by the interaction between these mechanisms is strongly desired to extend the design degrees of freedom for intriguing wave phenomena. Here, we demonstrate a phononic metamaterial consisting of C-shaped elements that enables us to investigate interaction between Bragg scattering and local resonance. We show that by adding resonance scattering a topological band gap is opened from a Bragg scattering based Dirac cone, and its band gap is controlled by the resonance frequency of the cavities relative to the Dirac cone frequency. In addition, we show that topological band-gap opening induced by the Bragg scattering can be reversed into an ordinary state or vice versa by judicious inclusion of the local resonance. Scattering cross-section analysis elaborates the combined effect of the two mechanisms on topological states. By employing lossy resonant elements, we further demonstrate a lossy topological insulator capable of one-way sound propagation immune to sharp corners, potentially leading to an energy-harvesting topological insulator. Our results provide a critical understanding of topological phenomena involving coupled scattering mechanisms.