Fingerprints of Topology in a Bulk Exciton Spectrum

The nontrivial topology of an insulator is widely considered to be nearly synonymous with the existence of Dirac surface states at its boundary. While these surface states have attracted a lot of attention, the properties of the bulk of these materials are usually considered to be conventional. Here we argue that nontrivial topology has fingerprints in the spectrum of excitons formed in their bulk. We consider the Bernevig-Hughes-Zhang model, which can be tuned between topological and trivial regimes, and show that the hierarchy of levels drastically changes as one crosses through the topological phase transition. In particular, the nontrivial Berry physics of an electron-hole pair in the topological regime generically splits excitonic states with different angular momenta and reorganizes the entire spectrum.