  Atomically thin MoS2/graphene heterostructures are promising candidates for
nanoelectronic and optoelectronic technologies. Among different graphene
substrates, epitaxial graphene (EG) on SiC provides several potential
advantages for such heterostructures including high electronic quality, tunable
substrate coupling, wafer-scale processability, and crystalline ordering that
can template commensurate growth. Exploiting these attributes, we demonstrate
here the thickness-controlled van der Waals epitaxial growth of MoS2 on EG via
chemical vapor deposition, giving rise to transfer-free synthesis of a
two-dimensional heterostructure with registry between its constituent
materials. The rotational commensurability observed between the MoS2 and EG is
driven by the energetically favorable alignment of their respective lattices
and results in nearly strain-free MoS2, as evidenced by synchrotron X-ray
scattering and atomic-resolution scanning tunneling microscopy (STM). The
electronic nature of the MoS2/EG heterostructure is elucidated with STM and
scanning tunneling spectroscopy, which reveals bias-dependent apparent
thickness, band bending, and a reduced bandgap of ~0.4 eV at the monolayer MoS2
edges.
