Theory of moiré localized excitons in transition metal dichalcogenide heterobilayers

Transition-metal dichalcogenide heterostructures exhibit moiré patterns that spatially modulate the electronic structure across the material's plane. For certain material pairs, this modulation acts as a potential landscape with deep, trigonally symmetric wells capable of localizing interlayer excitons, forming periodic arrays of quantum emitters. Here, we study these moiré localized exciton states and their optical properties. By numerically solving the two-body problem for an interacting electron-hole pair confined by a trigonal potential, we compute the localized exciton spectra for different pairs of materials. We derive optical selection rules for the different families of localized states, each belonging to one of the irreducible representations of the potential's symmetry group C3v, and numerically estimate their polarization-resolved absorption spectra. We find that the optical response of localized moiré interlayer excitons is dominated by states belonging to the doubly degenerate E irreducible representation. Our results provide insights into the optical properties of artificially confined excitons in two-dimensional semiconductors.