  Understanding the origin of valence band maxima (VBM) splitting in transition
metal dichalcogenides (TMDs) is important because it governs the unique spin
and valley physics in monolayer and multilayer TMDs. In this work, we present
our systematic study of VBM splitting ($\Delta$) in atomically thin MoS$_2$ and
WS$_2$ by employing photocurrent spectroscopy as we change the temperature and
the layer numbers. We found that VBM splitting in monolayer MoS$_2$ and WS$_2$
depends strongly on temperature, which contradicts the theory that spin-orbit
coupling solely determines the VBM splitting in monolayer TMDs. We also found
that the rate of change of VBM splitting with respect to temperature
($m=\frac{\partial\Delta}{\partial T}$) is the highest for monolayer (-0.14
meV/K for MoS$_2$) and the rate decreases as the layer number increases ($m ~
0$ meV/K for 5 layers MoS$_2$). We performed density functional theory (DFT)
and the GW with Bethe-Salpeter Equation (GW-BSE) calculations to determine the
electronic band structure and optical absorption for a bilayer MoS$_2$ with
different interlayer separations. Our simulations agree with the experimental
observations and demonstrate that the temperature dependence of VBM splitting
in atomically thin monolayer and multilayer TMDs originates from the changes in
the interlayer coupling strength between the neighboring layers. By studying
two different types of TMDs and many different layer thicknesses, we also
demonstrate that VBM splitting also depends on the layer numbers and type of
transition metals. Our study will help understand the role spin-orbit coupling
and interlayer interaction play in determining the VBM splitting in quantum
materials and develop next-generation devices based on spin-orbit interactions.
