Topological Wannier excitons in bismuth chalcogenide nanosheets I: Single-particle properties

We analyze the topology and dispersion of bulk Wannier excitons in nanosheets of topological insulators in the family of bismuth chalcogenides. Our main finding is that excitons also inherit the topology of the electronic bands, quantified by the skyrmion winding numbers of the constituent electron and hole pseudospins as a function of the total exciton momentum. We furthermore show that every $s$-wave exciton state consists of a quartet with a degenerate and quadratically dispersing nonchiral doublet, and a chiral doublet with one linearly dispersing mode as in transition metal dichalcogenides. We also demonstrate the existence of topological edge states of chiral excitons arising from the bulk-boundary correspondence.