Controlling Sound Wave Propagation in Topological Crystalline Insulators and Rainbow-Trapping

Topological crystalline insulators (TCIs) capable of supporting topological states protected by spatial symmetries have given rise to a promising platform for wave manipulation due to their robustness. Unfortunately, the methods to control the group velocity of topological states in classical wave systems are rarely discussed, which is an important issue in practical applications. In this work, we propose a method to change the frequency and propagation speed of topological edge states through on-site potential and realize a prototype of topological rainbow concentrator in a resonant acoustic system at subwavelength, which can separate different frequency components of propagating sound waves. The concepts of classical wave systems are combined with condensed matter physics, and the rigorous correspondence of TCIs and their analogs in acoustic resonant systems is demonstrated to design topological acoustic devices. Further, the implementation of controlling the group velocity of topological states precisely in a two-dimensional Su-Schrieffer-Heeger model is presented in detail, which can be extended to other TCI models and higher dimensions. We hope this work will enlarge possible applications of topological phenomena and the manufacture of acoustic devices.