Interlayer hybridization and moiré superlattice minibands for electrons and excitons in heterobilayers of transition-metal dichalcogenides

Geometrical moir\'e patterns, generic for almost aligned bilayers of two-dimensional crystals with similar lattice structure but slightly different lattice constants, lead to zone folding and miniband formation for electronic states. Here, we show that moir\'e superlattice (mSL) effects in $\mathrm{MoSe}{}_{2}/\mathrm{WS}{}_{2}$ and $\mathrm{MoTe}{}_{2}/\mathrm{MoSe}{}_{2}$ heterobilayers that feature alignment of the band edges are enhanced by resonant interlayer hybridization, and anticipate similar features in twisted homobilayers of transition-metal dichalcogenides (TMDs), including examples of narrow minibands close to the actual band edges. Such hybridization determines the optical activity of interlayer excitons in TMD heterostructures, as well as energy shifts in the exciton spectrum. We show that the resonantly hybridized exciton energy should display a sharp modulation as a function of the interlayer twist angle, accompanied by additional spectral features caused by umklapp electron-photon interactions with the mSL. We analyze the appearance of resonantly enhanced mSL features in absorption and emission of light by the interlayer exciton hybridization with both intralayer $A$ and $B$ excitons in $\mathrm{MoSe}{}_{2}/\mathrm{WS}{}_{2}, \mathrm{MoTe}{}_{2}/\mathrm{MoSe}{}_{2}, \mathrm{MoSe}{}_{2}/\mathrm{MoS}{}_{2}, \mathrm{WS}{}_{2}/\mathrm{MoS}{}_{2}$, and $\mathrm{WSe}{}_{2}/\mathrm{MoSe}{}_{2}$.