Voltage-controlled quantum valley Hall effect in dielectric membrane-type acoustic metamaterials

The research interest on phononic crystals now takes a new turn towards the acoustic/elastic analogies of the quantum concepts, e.g., the quantum Hall, quantum spin Hall and quantum valley Hall effects. One hallmark of these fundamental physical phenomena is the existence of topological edge/interface modes that propagate through the system along a designed path, with high robustness against week disorders. However, the working frequency ranges of the proposed topological phononic systems are usually very narrow, which therefore pose a clear limitation in practical applications. Motivated by this difficulty, we design and study a membrane-type metamaterial with tunable topological properties. The plane wave expansion method is employed to analyze its dispersion relation. A theoretical method is further proposed to conveniently calculate the valley Chern number. The theoretical and numerical results show the existence of topologically protected interface mode in the system. Its frequency range can be changed over a wide range by applying an electrical voltage, while the localization behavior of the interface mode is independent of the controlling operation. Consequently, we have successfully shown that the working frequency range of the topological phononic systems so derived can be significantly `broadened' and hence the practical application may be dramatically widened.