Acoustic transport in higher-order topological insulators with Dirac hierarchy

Dirac cones (DCs) are an important band structure in topological insulators (TIs) for realizing topological phase transition, and they provide unique ways to artificially regulate wave transport. Herein, we proposed a simple method to achieve Dirac hierarchy in three-dimensional (3D) acoustic TIs with rich and controllable topological phase transitions. The split of multifold DCs in each bulk Dirac hierarchy induced boundary Dirac hierarchy, including topological surface states and topological hinge states. We successfully realized 3D higher-order topological insulators (HOTIs) that exhibited two-fold boundary Dirac hierarchy with hinge states and achieved energy transport along three independent directions based on hinge-to-hinge channels. The proposed method is not limited to single hinges, and it provides a new design idea for multidimensional sound transport, serving as the basis for controllable acoustic functional devices.