Evolution of interlayer coupling in twisted molybdenum disulfide bilayers
Van der Waals (vdW) coupling is emerging as a powerful method to engineer and tailor physical properties of atomically thin two-dimensional (2D) materials. In graphene/graphene and graphene/boron-nitride structures it leads to interesting physical phenomena ranging from new van Hove singularities and Fermi velocity renormalization to unconventional quantum Hall effects and Hofstadter's butterfly pattern. 2D transition metal dichalcogenides (TMDCs), another system of predominantly vdW-coupled atomically thin layers can also exhibit interesting but different coupling phenomena because TMDCs can be direct or indirect bandgap semiconductors. Here, we present the first study on the evolution of interlayer coupling with twist angles in as-grown MoS 2 bilayers. We find that an indirect bandgap emerges in bilayers with any stacking configuration, but the bandgap size varies appreciably with the twist angle: it shows the largest redshift for AA- and AB-stacked bilayers, and a significantly smaller but constant redshift for all other twist angles. The vibration frequency of the out-of-plane phonon in MoS 2 shows similar twist angle dependence. Furthermore, our observations, together with ab initio calculations, reveal that this evolution of interlayer coupling originates from the repulsive steric effects, which leads to different interlayer separations between the two MoS 2 layers in different stacking configurations.