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We analyze the topology and dispersion of bulk Wannier excitons in nanosheetsof topological insulators in the family of bismuth chalcogenides. Our mainfinding is that excitons also inherit the topology of the electronic bands,quantified by the skyrmion winding numbers of the constituent electron and holepseudospins as a function of the total exciton momentum. We furthermore showthat every $s$-wave exciton state consists of a quartet with a degenerate andquadratically dispersing nonchiral doublet, and a chiral doublet with onelinearly dispersing mode as in transition metal dichalcogenides. We alsodemonstrate the existence of topological edge states of chiral excitons arisingfrom the bulk-boundary correspondence.

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