  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.
