Gauge-field-induced duality group in metamaterials

Dualities are mappings that connect seemingly unrelated physical systems, enabling simplification and reinterpretation via duality transformations. However, prior studies have been predominantly limited to one-to-one mappings isomorphic to a $Z_2$ group, where self-duality occurs only at a single point at which the lattice maps onto itself under a duality transformation. Here, we extend the duality framework by incorporating gauge fields that modify symmetry representations, constructing more general duality groups, $Z_2\times Z_2$ in two-dimensional systems and ${\left(Z_2\right)}^6$ in three-dimensional systems. We theoretically establish and experimentally validate that such gauge-field-induced duality groups link multiple distinct metamaterials across different symmetry classifications while sharing identical band structures. Notably, in three-dimensional systems, gauge fields promote self-duality from a single point to a set, yielding fourfold degeneracies across the entire Brillouin zone and an eightfold-degenerate double Dirac point. Our work expands duality research and deepens the understanding of hidden symmetries in complex physical systems.