Theory of optical absorption by interlayer excitons in transition metal dichalcogenide heterobilayers

We present a theory of optical absorption by interlayer excitons in a heterobilayer formed from transition metal dichalcogenides. The theory accounts for the presence of small relative rotations that produce a momentum shift between electron and hole bands located in different layers, and a moir\'e pattern in real space. Because of the momentum shift, the optically active interlayer excitons are located at the moir\'e Brillouin zone's corners, instead of at its center, and would have elliptical optical selection rules if the individual layers were translationally invariant. We show that the exciton moir\'e potential energy restores circular optical selection rules by coupling excitons with different center of mass momenta. A variety of interlayer excitons with both senses of circular optical activity, and energies that are tunable by twist angle, are present at each valley. The lowest energy exciton states are generally localized near the exciton potential energy minima. We discuss the possibility of using the moir\'e pattern to achieve scalable two-dimensional arrays of nearly identical quantum dots.