Gauge-field-induced duality group in metamaterials.

Abstract

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 <math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mrow><mi>Z</mi></mrow><mrow><mn>2</mn></mrow></msub></math> 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, <math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mrow><mi>Z</mi></mrow><mrow><mn>2</mn></mrow></msub><mo>×</mo><msub><mrow><mi>Z</mi></mrow><mrow><mn>2</mn></mrow></msub></math> in two-dimensional systems and <math xmlns="http://www.w3.org/1998/Math/MathML"><msup><mrow><mfenced><mrow><msub><mrow><mi>Z</mi></mrow><mrow><mn>2</mn></mrow></msub></mrow></mfenced></mrow><mrow><mn>6</mn></mrow></msup></math> 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.