Angular dependence of the interlayer coupling at the interface between two dimensional materials 1T-PtSe${}_2$ and graphene

We present a study by Scanning Tunneling Microscopy, supported by ab initio calculations, of the interaction between graphene and monolayer (semiconducting) PtSe${}_2$ as a function of the twist angle $\theta$ between the two layers. We analyze the PtSe${}_2$ contribution to the hybrid interface states that develop within the bandgap of the semiconductor to probe the interaction. The experimental data indicate that the interlayer coupling increases markedly with the value of $\theta$, which is confirmed by ab initio calculations. The moiré patterns observed within the gap are consistent with a momentum conservation rule between hybridized states, and the strength of the hybridization can be qualitatively described by a perturbative model.