Band engineering in twisted molybdenum disulfide bilayers

In order to explore the theoretical relationship between interlayer spacing, interaction and band offset at the atomic level in vertically stacked two-dimensional (2D) van der Waals (vdW) structures, we propose an analytical model to address the evolution of interlayer vdW coupling with random stacking configurations in MoS2 bilayers based on the atomic-bond-relaxation correlation mechanism. We found that interlayer spacing changes substantially with respect to the orientations, and the bandgap increases from 1.53 eV (AB stacking) to 1.68 eV (AA stacking). Our results reveal that the evolution of interlayer vdW coupling originates from the interlayer interaction, leading to interlayer separations and electronic properties changing with stacking configurations. Our predictions constitute a demonstration of twist engineering the band shift in the emergent class of 2D crystals, transition-metal dichalcogenides.