Bandgap inhomogeneity of MoS$_2$ monolayer on epitaxial graphene bilayer in van der Waals p-n junction

Atomically thin MoS$_2$/graphene vertical heterostructures are promising candidates for nanoelectronic and optoelectronic technologies.In this work, we studied the optical and electronic properties of n doped single layer MoS$_2$ on p doped bilayer graphene vdW heterostructures. We demonstrate a non-uniform strain between two different orientation angles of MoS$_2$ monolayer on top of epitaxial bilayer gra-phene. A significant downshift of the E$^1$$_{2_g}$ mode, a slight downshift of the A$_{1_g}$ mode, and photo-luminescence shift and quenching are observed between two MoS$_2$ monolayers differently oriented with respect to graphene; This could be mostly attributed to the strain-induced transition from direct to indirect bandgap in monolayer MoS$_2$. Moreover, our theoretical calculations about differently-strained MoS$_2$ monolayers are in a perfect accordance with the experimentally observed behavior of differently-oriented MoS$_2$ flakes on epitaxial bilayer graphene. Hence, our results show that strain-induced bandgap engineering of single layered MoS$_2$ is dependent on the orientation angle between stacked layers. These findings could be an interesting novel way to take advantage of the possibilities of MoS$_2$ and deeply exploit the capabilities of MoS$_2$/graphene van der Waals heterostructures.