  The possibility of engineering experimentally viable systems that realize
gauge fluxes within plaquettes of hopping have been subject of 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 mid-gap states. These modes can hybridize in extended flux
lattices, giving rise to semi-metallic bands that are highly tunable. We
demonstrate that within artificial materials, local $\pi$-fluxes can be
naturally realized. Consequently, we provide concrete set-ups to access this
physics and analyze similar self-organized band structures and physical
properties. Our work therefore does not only pinpoint simple systems exhibiting
flat bands, but also opens up a route to study flux lattice models and
associated effective theories in a novel scene.
