Thermally tunable topological edge states for in-plane bulk waves in solid phononic crystals

The remarkable properties of topological insulators have inspired numerous studies on topological transport for bulk waves, but the demonstrations of topological edge states with tunable frequency are few attempts. Here, we report on the active frequency tunability of topologically protected edge states for in-plane bulk waves by applying a thermal field. We find that the center frequency of topological band gap is shifted down and the band width is enlarged as the temperature increases. Meanwhile, the frequency range of topologically protected edge states is also shifted to low frequency region with the higher temperature. Furthermore, the robust propagation of in-plane bulk waves along a desired path is demonstrated within different frequency bands. The tunable frequency for both topological band gaps and topologically protected edge states achieves the active control of the transport for in-plane bulk waves, which may dramatically facilitate practical applications of novel phononic devices.