Angle dependence of the local electronic properties of the graphene/MoS$_2$ interface determined by $\it ab$ $\it initio$ calculations

We present a full theoretical study of the graphene/MoS$_2$ interface, using density functional theory (DFT) calculations and scanning tunneling microscopy (STM) simulations. In particular, we show that contrary to previous theoretical predictions, the rotation angle between the layers has no influence on the global electronic properties of the interface, providing a careful choice of lattice vectors and supercells is made, in order to avoid artificial modifications in the electronic structure. However, small modifications of the local electronic properties do appear, as revealed by the calculated STM images. This result might be exploited in nanoelectronic devices by specific local contacting.