π-fluxes, semimetals, and flat bands in artificial materials

The possibility of engineering experimentally viable systems that realize gauge fluxes within plaquettes of hopping has been the subject of a search for decades due to vast amounts of theoretical study. This is of particular interest for topological band insulators, where it is known that such fluxes bind protected midgap states. These modes can hybridize in extended flux lattices, giving rise to semimetallic bands that are highly tunable. We demonstrate that within artificial materials, local pi-fluxes can be naturally realized. Also, the importance of the crystalline symmetry for protecting the pi-flux modes is pointed out. Consequently, we provide concrete setups and conditions to access this physics and analyze similar self-organized band structures and physical properties. Our work therefore not only pinpoints simple systems exhibiting flat bands but also opens up a route to study flux lattice models and associated effective theories.