  Despite the weak nature of interlayer forces in transition metal
dichalcogenide (TMD) materials, their properties are highly dependent on the
number of layers in the few-layer two-dimensional (2D) limit. Here, we present
a combined scanning tunneling microscopy/spectroscopy and GW theoretical study
of the electronic structure of high quality single- and few-layer MoSe2 grown
on bilayer graphene. We find that the electronic (quasiparticle) bandgap, a
fundamental parameter for transport and optical phenomena, decreases by nearly
one electronvolt when going from one layer to three due to interlayer coupling
and screening effects. Our results paint a clear picture of the evolution of
the electronic wave function hybridization in the valleys of both the valence
and conduction bands as the number of layers is changed. This demonstrates the
importance of layer number and electron-electron interactions on van der Waals
heterostructures, and helps to clarify how their electronic properties might be
tuned in future 2D nanodevices.
