Topological excitons are superpositions of electron-hole pair states, characterized by an envelope function with finite vorticity in momentum space. This vorticity is determined by the underlying topology of the electronic bands. We derive the optical selection rules for topological excitons in flat bands, considering different topological two-band models: a family of Hamiltonians with skyrmion pseudo-spin textures, the flattened BHZ model for a single spin, and the flattened Haldane model. We derive the selection rules for these three models accounting for short-range interactions. We also consider the nonhydrogenic spectrum of excitons in the single-spin flattened BHZ model with Coulomb interactions. We show that, for the case of two flat bands with skyrmion pseudo-spin textures, all excitons are bright, and the handedness of the light that couples to them is the same as the vorticity of the pseudo-spin texture. For the single-spin flattened BHZ model, we show that bright excitons couple to circularly polarized light, regardless of the range of the interactions. In the flattened Haldane model, topological excitons couple to elliptically polarized light. We obtain the phase diagram for the polarization of light in this model as a function of microscopic parameters of the Hamiltonian. Our results demonstrate how band topology affects exciton properties, offering a framework for predicting light-matter interactions in topological materials with flat bands.

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• Excitons
• Flat bands
• Topological materials
• 2-dimensional systems