Interlayer Electronic Coupling in Arbitrarily Stacked MoS2 Bilayers Controlled by Interlayer S-S Interaction

The vertically heterostructured MoS2 bilayers display a wide range of lattice registry relative to bulk MoS2 through a single or combined in-plane displacement, out-of-plane displacement, and in-plane rotation. Here using density functional theory and numerical structural analysis, we examine both the atomic and electronic structures of the arbitrarily stacked MoS2 bilayers that form either commensurate or incommensurate superstructures. Our analysis shows that the interlayer electronic coupling between two MoS2 layers yields an indirect band gap that varies with the lattice registry, thus confirming the previous theoretical findings. The variation of the coupling strength and the indirect band gap with respect to the lattice registry can be attributed to the change in the mean interlayer sulfursulfur distance upon displacement. Importantly, our analysis further shows when the twisted MoS2 bilayers form an incommensurate structure, the interlayer sulfursulfur distance is uniformly sampled in-plane and yields a distribution independent of the incommensurate twist angle. When a commensurate structure is formed, while the distribution becomes angular dependent, the mean in-plane sulfursulfur distance is found nearly independent of the twist angle. Consequently, the magnitude of the indirect band gap in the bilayers exhibits a weak angular dependence, until the twist angle recovers the high symmetry stacking sequence when the gap changes significantly. Our analysis provides the thorough theoretical explanation to the recently measured photoluminescence spectroscopy in twisted MoS2 bilayers and can form the basis for understanding the coupling in vertically heterostructured bilayers composed of other transition-metal dichalcogenide monolayers.