Designing Topological Bands in Reciprocal Space

Abstract: 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.