  In van der Waals heterostructures of two-dimensional transition-metal
dichalcogenides (2D TMDCs) electron and hole states are spatially localized in
different layers forming long-lived interlayer excitons. Here, we have
investigated, from first principles, the influence of additional electron or
hole layers on the electronic properties of a MoS2/WSe2 heterobilayer (HBL),
which is a direct band gap material. Additional layers modify the interlayer
hybridization, mostly affecting the quasiparticle energy and real-space extend
of hole states at the G and electron states at the Q valleys. For a sufficient
number of additional layers, the band edges move from K to Q or G,
respectively. Adding electron layers to the HBL leads to more delocalized Q
states, while G states do not extend much beyond the HBL, even when more hole
layers are added. These results suggest a simple and yet powerful way to tune
band edges and the real-space extend of the electron and hole wave function in
TMDC heterostructures, strongly affecting the lifetime and dynamics of
interlayer excitons.
