Acoustic rainbow trapping effect of double corner states in higher-order topological insulators

Higher-order topological insulators are a type of topological state of matter, which break the traditional bulk-edge correspondence principle. At the same time, the concept of higher-order topological states in condensed matter physics has rapidly extended to acoustic and optical systems and provided a new degree of freedom for controlling classical waves. However, capturing higher-order topological states of distinct frequencies at different geometric angles in acoustic systems remains a challenging problem. Based on sonic crystals with the “breathing” Kagome lattices, we theoretically and experimentally realize the acoustic rainbow trapping effect of double corner states. The Wannier centers of the upward and downward triangles are not in the same positions, which is conducive for arbitrarily adjusting the positions of the higher-order topological states. Our results offer a method for capturing multi-frequency acoustic waves and enhance the applications of higher-order topological states.