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It has recently been shown that quantum-confined states can appear inepitaxially grown van der Waals material heterobilayers without a rotationalmisalignment ($\theta=0^\circ$), associated with flat bands in the Brillouinzone of the moir\'e pattern formed due to the lattice mismatch of the twolayers. Peaks in the local density of states and confinement in aMoS$_2$/WSe$_2$ system was qualitatively described only considering localstacking arrangements, which cause band edge energies to vary spatially. Inthis work, we report the presence of large in-plane strain variation across themoir\'e unit cell of a $\theta=0^\circ$ MoS$_2$/WSe$_2$ heterobilayer, and showthat inclusion of strain variation and out-of-plane displacement in densityfunctional theory calculations greatly improves their agreement with theexperimental data. We further explore the role of twist-angle by showingexperimental data for a twisted MoS$_2$/WSe$_2$ heterobilayer structure withtwist angle of $\theta=15^\circ$, that exhibits a moir\'e pattern but noconfinement.

Flatbands and Mechanical Deformation Effects in the Moir\'e Superlattice of MoS$_2$-WSe$_2$ Heterobilayers