Hierarchical Topological States in Three Dimensional Phononic System

We have designed a novel three dimensional (3D) structural model for demonstrating higher order (HO) topological states of acoustic-wave propagation. Based on a stacked honeycomb structure, we show that two-dimensional (2D) surface state and one dimensional (1D) hinge state can be numerically designed through a hierarchical property of phononic band. Due to its simple stacking structure, the model presented here is expected to be easier for fabrication than the existing proposed models and thus may serve as a prototype for designing 3D integration of acoustic-wave devices for information transmission.