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 singularities1-4 and Fermi velocity renormalization5, 6 to unconventional quantum Hall effects7 and Hofstadter's butterfly pattern8-12. 2D transition metal dichalcogenides (TMDCs), another system of predominantly vdW-coupled atomically thin layers13, 14, can also exhibit interesting but different coupling phenomena because TMDCs can be direct or indirect bandgap semiconductors15, 16. Here, we present the first study on the evolution of interlayer coupling with twist angles in as-grown MoS2 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 MoS2 shows similar twist angle dependence. 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 MoS2 layers in different stacking configurations.

Van der Waals coupling is emerging as a powerful method to engineer physical properties of atomically thin two-dimensional materials. In coupled graphene-graphene and graphene-boron nitride layers, interesting physical phenomena ranging from Fermi velocity renormalization to Hofstadter's butterfly pattern have been demonstrated. Atomically thin transition metal dichalcogenides, another family of two-dimensional-layered semiconductors, can show distinct coupling phenomena. Here we demonstrate the evolution of interlayer coupling with twist angles in as-grown molybdenum disulfide bilayers. We find that the indirect bandgap size varies appreciably with the stacking configuration: it shows the largest redshift for AA- and AB-stacked bilayers, and a significantly smaller but constant redshift for all other twist angles. Our observations, together with ab initio calculations, reveal that this evolution of interlayer coupling originates from the repulsive steric effects that leads to different interlayer separations between the two molybdenum disulfide layers in different stacking configurations.