Multiple high-order topological states with high-order resonant bands in kagome lattice phononic crystal with resonant cavities

The topological phase of phononic crystals has garnered significant attention in the design of systems for confining and manipulating acoustic waves due to the robustness of topological states within bandgaps. In this work, we propose a kagome tight-binding model phononic crystal that utilizes the resonant effect coupling between cavities for airborne sound. The topological phase transition within high-order resonant bandgaps is achieved by tuning the coupling strength with the nontrivial phase characterized by a shrunken lattice. In an initial superstructure, we numerically calculate the eigenfrequencies and identify an effective configuration by adjusting the distance between cavities. This optimized structure facilitates multiple corner states with topological protection in two domains. The robustness of these corner states is confirmed through numerical simulations by introducing the disorder into optimized structure. Experimental results demonstrate that this setup can efficiently and robustly confine acoustic waves by leveraging the topological corner states derived from resonant effect in the fabricated sample. This approach not only realizes multiple high-order topological states but also offers enhanced flexibility for applications in acoustic wave manipulation and confinement.