Observation of Emergent Dirac Physics at the Surfaces of Acoustic Higher-Order Topological Insulators.

Using 3D sonic crystals as acoustic higher-order topological insulators (HOTIs), 2D surface states described by spin-1 Dirac equations at the interfaces between the two sonic crystals with distinct topology but the same crystalline symmetry are discovered. It is found that the Dirac mass can be tuned by the geometry of the two sonic crystals. The sign reversal of the Dirac mass reveals a surface topological transition where the surface states exhibit zero refractive index behavior. When the surface states are gapped, 1D hinge states emerge due to the topology of the gapped surface states. The zero refractive index behavior and the emergent topological hinge states are confirmed experimentally. This study reveals a multidimensional Wannier orbital control that leads to extraordinary properties of surface states and unveils an interesting topological mechanism for the control of surface waves.