Gauge-field-induced duality group in metamaterials

Abstract Dualities are mathematical mappings that establish counterintuitive connections between two seemingly unrelated physical systems, enabling the simplification and reinterpretation of complex systems via duality transformations. Recent breakthroughs have revealed that dualities can enhance the symmetries of a Hamiltonian and facilitate the design of metamaterials with unprecedented properties that transcend conventional space group theory. However, prior studies on dualities have been predominantly limited to one-to-one mappings isomorphic to a Z_2 group, and the self-duality occurs only at a single point where the lattice maps onto itself under a duality transformation. Here, we extend the duality framework by incorporating gauge field degrees of freedom that modify symmetry representations in metamaterials, thereby constructing richer duality groups, Z_2⊗Z_2 in two-dimensional (2D) systems and ⊗┬6 Z_2 in three-dimensional (3D) systems. We theoretically establish and experimentally validate that such gauge-field-induced duality groups can link multiple distinct metamaterials across different symmetry classifications, while sharing the same band structures. More interestingly, in 3D systems, the introduction of gauge fields promotes the self-duality from a single point to an entire set, resulting in fourfold degeneracies across the entire Brillouin zone and supporting an emergent eightfold-degenerate double Dirac point. Our work expands the research frontier of duality and deepens the understanding of hidden symmetries and band degeneracies in complex physical systems.