Evolution of interlayer coupling in twisted molybdenum disulfide bilayers.

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.