  We present in-depth measurements of the electronic band structure of the
transition-metal dichalcogenides (TMDs) MoS2 and WS2 using angle-resolved
photoemission spectroscopy, with focus on the energy splittings in their
valence bands at the K point of the Brillouin zone. Experimental results are
interpreted in terms of our parallel first-principles computations. We find
that interlayer interaction only weakly contributes to the splitting in bulk
WS2, resolving previous debates on its relative strength. We additionally find
that across a range of TMDs, the band gap generally decreases with increasing
magnitude of the valence-band splitting, molecular mass, or ratio of the
out-of-plane to in-plane lattice constant. Our results provide an important
reference for future studies of electronic properties of MoS2 and WS2 and their
applications in spintronics and valleytronics devices.
