Multidimensional Interface Topology Induced by Acoustic Wannier Configurations

Recently, real-space representations, revealing in depth the duality of topological descriptions in real and momentum space, have been applied to show multidimensional crystalline topology. Here we propose nontrivial phononic crystals by constructing different Wannier configurations based on real-space representations. We experimentally achieve the symmetry-protected interface topology in multiple dimensions containing anomalous interface states and higher-order corner states. Nontrivial acoustic pseudospin polarizations are critical to the interface states and have been directly observed in experiment. In a consistent frame, the higher-order corner states arising from the fractional charge anomaly are further observed. Our study provides a scheme based on Wannier configurations for designing topological metamaterials, which is fruitful for characterizing and manipulating multidimensional topological states and can be generalized to other classical systems.