The higher-order topological pumping explored in the 2D acoustic crystal

The topological pumping has been instrumental in advancing our understanding of topological phase transitions in various physical systems, which can be extended to uncover intriguing higher-order topological phases in the lower-dimensional system. Here, we propose a theoretical exploration of topological dipole pumping on an acoustic square superlattice by cyclically modulating intracell couplings, which shares the topological nature of an extended three-dimensional system with chiral hinge states. Using the multipole chiral numbers, we characterize the higher-order topological phases that arise during the evolution. The evolution of topological phase transitions is verified by numerical simulations and shows corner states are transferred across the bulk. Our findings can inspire the construction of chiral hinge states in artificial crystals, opening up new possibilities for the design of devices allowing the unidirectional propagation of sound.