Realization of multidimensional sound propagation in 3D acoustic higher-order topological insulator

Higher-order topological insulators (TIs) develop the conventional bulk-boundary correspondence theory and increase the interest in searching innovative topological materials. To realize a higher-order TI with a wide passband of one-dimensional (1D) and two-dimensional (2D) transportation modes, we design three-dimensional non-trivial and trivial sonic crystals whose combination mimics the Su-Schrieffer-Heeger model. The topological boundary states can be found at the interfaces, including the zero-dimensional corner state, 1D hinge state, and 2D surface state. The fabricated sample with the bent two-dimensional and one-dimensional acoustic channels exhibits the multidimensional sound propagation and verifies the mode transition among the complete bandgap, hinge mode, and surface mode. The bandwidth of the single-mode hinge state achieves a large relative bandwidth of 9.1% in which sound transports one-dimensionally without significant leak into the surfaces or the bulk. The higher-order topological states in the study pave the way for sound manipulation in multiple dimensions.