Topological non-reciprocity provides a robust approach to control the wave field. To realize reversible topological non-reciprocity in chiral metamaterials, researchers usually rely on reversing angular momentum bias of the circulation flow, time reversing the spatiotemporal modulation, and so on. Here, we demonstrate that switching Poisson's ratio from positive to negative can reverse the topological non-reciprocity by mechanically stretching and compressing a chiral acoustic metamaterial. We find that the positive–negative switch of Poisson's ratio is associated with the topological phase transition of the acoustic lattice, which is manifested as the reversed propagation of topological edge modes. The reversed topological non-reciprocity of metamaterials is attributed to the transmission switch of the three-port chiral unit. Finally, we propose a design of topological wave splitters, in which transmission directions are adjusted by the Poisson's ratio of the device. Our results indicate that the Poisson's ratio of metamaterials can introduce peculiar topological properties and bring potential applications for wave isolators, modulators, and circulators.
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