Higher-order topological transport protected by boundary Chern number in phononic crystals

Abstract Topological pumps enable robust transports of topological states when the system parameters are varied in a cyclic process. The reported topological pumps are protected by the bulk topology. However, the exploration of topological pump protected by other mechanism remains elusive. Here we report our prediction and observation of higher-order topological pumps linked to the boundary topology, i.e., boundary Chern number. Based on such topological pump, the higher-order transports between the topological states of different dimensions (e.g., corner-edge-corner) are directly observed by spatial scanning of the sound field, and their topological robustness is observed in the paths with defects. Furthermore, modulated by the fundamental corner-edge-corner topological transport, topological splitting effects are unambiguously observed in our acoustic experiments. Our findings not only advance the research of the higher-order topological transports, but also offer good platforms to design unconventional devices.