Dual-band higher-order topological states in composite square-lattice sonic crystals

The discovery of higher-order topological insulator metamaterials has enriched fundamental schemes of classical wave manipulations. A common way of inducing higher-order topological wave phenomena is based on the original ${C}_{n}$-symmetric lattice characterized by a quantized Wannier center, which generally supports the higher-order topological states in a single band gap. Here, we report the acoustic realization of dual-band second-order topological insulators in ${C}_{4v}$-symmetric composite lattices, created by inserting extra sites into each inversion center of four adjacent unit cells of the original two-dimensional Su-Schrieffer-Heeger lattice. Due to the hybrid operation, we can create distinct nontrivial boundaries along the inserted sites, and multiple acoustic localized states occur in two band gaps simultaneously. Relying on two square-shaped sonic crystals with nontrivial boundaries, we experimentally verify the diverse state localizations on the corners and edges of the sonic crystals, and distinct phase profiles are observed for the boundary states in different band gaps. The topological robustness of corner and edge states under bulk disorder is experimentally demonstrated in comparison with the measured spectra of relevant boundary disorders. Our work opens an avenue to develop multifrequency acoustic devices, which may facilitate useful applications of multiband acoustic sensors and energy trapping.