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We investigate the optical properties of spin-triplet interlayer excitons inheterobilayer transition metal dichalcogenides in comparison with thespin-singlet ones. Surprisingly, the optical transition dipole of thespin-triplet exciton is found to be in the same order of magnitude to that ofthe spin-singlet exciton, in sharp contrast to the monolayer excitons where thespin triplet species is considered as dark compared to the singlet. Unlike themonolayer excitons whose spin-conserved (spin-flip) transition dipole can onlycouple to light of in-plane (out-of-plane) polarization, such restriction isremoved for the interlayer excitons due to the breaking of the out-of-planemirror symmetry. We find that as the interlayer atomic registry changes, theoptical transition dipole of interlayer exciton crosses between in-plane onesof opposite circular polarization and the out-of-plane one for both thespin-triplet and spin-singlet species. As a result, excitons of both specieshave non-negligible coupling into photon modes of both in-plane andout-of-plane propagations, another sharp difference from the monolayers wherethe exciton couples predominantly into the out-of-plane propagation channel. Atgiven atomic registry, the spin-triplet and spin-singlet excitons have distinctvalley polarization selection rules, allowing the selective optical addressingof both the valley configuration and the spin singlet/triplet configuration ofinterlayer excitons.

Brightened spin-triplet interlayer excitons and optical selection rules in van der Waals heterobilayers