Topological phononic crystals with tunable interface state based on local resonance

We propose a design for topological phononic crystals comprising Helmholtz resonators to give rise to tunable interface states by adjusting the side length and rotation angle of the cavities. The underlying mechanism is that the modulation of edge modes changes the interface state by controlling local resonance elements and breaking mirror symmetry. The performance of the resulting device is numerically demonstrated via the production of robust topological valley transport along a prescribed path for incident waves of different frequencies. Our design helps to improve the design of tunable topological insulators and may find important applications in diverse fields such as acoustic communications.