Optical selection rules for topological excitons in flat Chern bands

Topological excitons are bound states of electron-hole pairs that have a finite vorticity in momentum space. In two spatial dimensions, the vorticity of excitons is finite when the conduction and valence bands are topologically distinct, with the vorticity being equal to the difference of their Chern numbers. In this talk, we address the spectrum of topological excitons in the Brillouin zone and their optical selection rules. Topological excitons have distinct selection rules compared to the ones for particle-hole pairs in transition metal dichalchogenides, where circularly polarized light selectively couples with the valleys. Because the vorticity of topological excitons is a global property of their profile wave function in the whole Brillouin zone, all excitons will selectively couple with the same polarization of circularly polarized light. We identify experimental signatures of topological excitons for optical probes in Chern insulators.