Three-dimensional acoustic metamaterials with topological states of different orders and multidirectional waveguiding

The attainment of high-quality wave concentration and manipulation has always been considered as state-of-the-art technology, especially for integrated photonics and phononics. However, the prevention of energy loss caused by backscattering or imperfections remains a grand challenge. With the development of the topological phase of matter, the emergence of topological insulators that support robust conductive edge states but insulating bulk waves provides a possible solution. Nevertheless, the existing topological insulators can only achieve wave manipulation in two-dimensional (2D) models along specific hinges. To achieve lossless waveguiding in three-dimensional space, an acoustic topological insulator with three degrees of freedom is established. The theoretical dispersion relation is analyzed by introducing an equivalent electric circuit system. The topological states, including point corner states, one-dimensional hinge states, and 2D surface states are realized by tweaking the intra- and intercell couplings. Abundant wave propagation behaviors such as surface-restricted, edge-restricted, and corner-restricted wave transportation are respectively achieved in the first-, second-, and third-order topological insulators. The twisted 3D path waveguiding without significant energy leaking into surface and bulk is finally demonstrated. This sound transportation phenomenon may provide a paradigm and design idea for integrated acoustic devices with unconventional functions.