Band renormalization of a polymer physisorbed on graphene investigated by many-body perturbation theory

Many-body perturbation theory at the $G_0W_0$ level is employed to study the electronic properties of poly(\emph{para}-phenylene) (PPP) on graphene. Analysis of the charge density and the electrostatic potential shows that the polymer-surface interaction gives rise to the formation of only weak surface dipoles with no charge transfer between the polymer and the surface. In the local-density approximation (LDA) of density-functional theory, the band structure of the combined system appears as a superposition of the eigenstates of its constituents. Consequently, the LDA band gap of PPP remains unchanged upon adsorption onto graphene. $G_0W_0$ calculations, however, renormalize the electronic levels of the weakly physisorbed polymer. Thereby, its band gap is considerably reduced compared to that of the isolated PPP chain. This effect can be understood in terms of image charges induced in the graphene layer, which allows us to explain the quasi-particle gap of PPP versus polymer-graphene distance by applying a classical image-potential model. For distances below 4.5 Å, however, deviations from this simple classical model arise which we qualitatively explain by taking into account the polarizablity of the adsorbate. For a quantitative description with predictive power, however, we emphasize the need for an accurate ab-initio description of the electronic structure for weakly coupled systems at equilibrium bonding distances.