Modulation of optical selection rules in twisted transition metal dichalcogenide heterobilayer.

TMDCs of group 6 transition metals MX₂ (M = Mo, S, X = S, Se) exhibit layered structures with pronounced interlayer interactions, ideal for studying interlayer excitons in their van der Waals heterostructures. As their heterobilayers are incommensurable, moiré structures are present even if stacked without a twist angle. However, a comprehensive understanding of spin-valley physics at the moiré scale and its modification via twisted angles is yet to be fully explored. In this work, we explored the structural and electronic properties of these heterobilayers as function of the twist angle. We observe significant lattice reconstruction involving in- and out-of-plane relaxations, which strongly depend on the twist angle. This leads to different excitonic behaviour when compared to high-symmetry stackings. To gain a deeper insight into their excitonic behaviors, we examine the spin (S_z) and orbital (L_z) degrees of freedom of low-energy bands. We find that these depend on the consisting layers, and can be further modified by twist angles. Notably, the lattice reconstruction at small twist angles modulates the moiré minibands resulting in different optical selection rules. This implies that the optical selection rules in heterobilayers are determined not only by the high-symmetry stackings, but also by the relaxation effect in the moiré superlattice. In conclusion, we show how the twist angle as a new degree of freedom can be utilized to manipulate the interlayer excitons in the moiré structures.