Electron-electron interactions in the vacuum polarization of graphene

We discuss the effect of electron-electron interactions on the static polarization properties of graphene beyond RPA. Divergent self-energy corrections are naturally absorbed into the renormalized coupling constant alpha. We find that the lowest-order vertex correction, which is the first nontrivial correlation contribution, is finite, and about 30% of the RPA result at strong coupling alpha similar to 1. The vertex correction leads to further reduction of the effective charge. Finite contributions to dielectric screening are expected in all orders of perturbation theory.