Chiral Topological Excitons in a Chern Band Insulator

A family of semiconductors called as Chern band insulator are shown to host exciton bands with non-zero topological Chern integers and chiral exciton edge modes. Using a prototypical two-band Chern insulator model, we calculate a cross-correlation function to obtain the exciton bands and their Chern integers. The lowest exciton band acquires Chern integers such as $\pm 1$ and $\pm 2$ in electronic Chern insulator phase. The non-trivial topology can be experimentally observed both by non-local optoelectronic response of exciton edge modes and by a phase shift in the cross-correlation response due to the bulk mode. Our result suggests that magnetically doped HgTe, InAs/GaSb quantum wells and $\text{(Bi,Sb)}_{2} \text{Te}_{3}$ thin film are promising candidates for a platform of topological excitonics.