Designing Topological Bands in Reciprocal Space

Motivated by new capabilities to realise artificial gauge fields in ultracold atomic systems, and by their potential to access correlated topological phases in lattice systems, we present a new strategy for designing topologically non-trivial band structures. Our approach is simple and direct: it amounts to considering tight-binding models directly in reciprocal space. These models naturally cause atoms to experience highly uniform magnetic flux density and lead to topological bands with very narrow dispersion, without fine-tuning of parameters. Further, our construction immediately yields instances of optical Chern lattices, as well as band structures of higher Chern number, |C|>1.