# $\pi$-fluxes, semi-metals and flat bands in artificial materials

## TL;DR

This paper explores how artificial materials can naturally realize local $$-fluxes, leading to tunable semi-metallic bands and flat bands, providing new platforms for studying flux lattice physics and topological states.

## Contribution

It demonstrates the natural realization of $$-fluxes in artificial materials and proposes concrete setups to explore flux lattice models and their physical properties.

## Key findings

- Local $$-fluxes can be realized in artificial materials.
- Flux lattices lead to semi-metallic and flat band structures.
- Provides new routes to study topological and flux lattice physics.

## Abstract

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.