Experimental Realization of Synthetic π-Flux Photonic Crystals

The concept of flux in quantum physics is connected to many intriguing phenomena such as the Aharonov-Bohm effect and Hofstadter butterfly. Particularly, flux in lattices with certain symmetries gives rise to many unprecedented phases of matter. Here, we report the experimental realization of two-dimensional photonic crystals featuring diverse synthetic π-flux patterns, achieved through harnessing the higher-orbital degree of freedom within confined-Mie-resonance photonic crystals. As a proof of concept, we fabricate two types of π-flux photonic crystals, and show that novel topological phases can emerge with peculiar optical effects, including a topological edge state with 4π-period phase evolution, as well as two pairs of topological states which are localized at opposite boundaries but related by a nonlocal twist. These signatures characterize unambiguously a photonic Möbius insulator [an insulator with topological edge states with a 4π-periodic sideband junction (like a Möbius ring)] and a momentum-space-nonsymmorphic symmetry characterized insulator, which remain experimentally unexplored to date. Our Letter opens the frontiers to explore the underlying physics between synthetic π-flux and photonic crystals.