Topological excitons in moiré MoTe$_2$/WSe$_2$ heterobilayers

Due to the presence of flat Chern bands, moiré transition metal dichalcogenide (TMD) bilayers are a platform to realize strongly correlated topological phases of fermions such as fractional Chern insulators. TMDs are also known to host long-lived excitons, which inherit the topology of the underlying Chern bands. For the particular example of MoTe$_2$/WSe$_2$ heterobilayers we perform a time-dependent Hartree-Fock calculation to identify a regime in the phase diagram where the excitons themselves form a topological flat band. This paves a way towards realizing strongly correlated states of bosons in moiré TMDs.