Research on dualities is commonly restricted to one-to-one mappings. Here, by incorporating artificial gauge fields, the authors demonstrate 2D and 3D acoustic metamaterials enabling ℤ2 × ℤ2 and (ℤ2)6 duality groups, respectively, where distinct structures share identical band structures, and self-duality gives rise to symmetry-protected high-order degeneracies.
- Yan Meng
- Hong-yu Zou
- Zhen Gao