Electron-Electron Interactions in the Vacuum Polarization of Graphene

TL;DR

This paper investigates how electron-electron interactions influence the static polarization and dielectric screening in graphene, revealing that vertex corrections reduce the effective charge and are finite at strong coupling, with implications for many-order perturbations.

Contribution

It provides the first finite calculation of the lowest order vertex correction beyond RPA in graphene, showing a significant reduction of the effective charge at strong coupling.

Findings

Vertex correction is about 30% of RPA at strong coupling

Divergent self-energy corrections are absorbed into the renormalized coupling

Finite contributions to dielectric screening persist at all orders

Abstract

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 non-trivial correlation contribution, is finite, and about 30% of the RPA result at strong coupling $\alpha \sim 1$. The vertex correction leads to further reduction of the effective charge. Finite contributions to dielectric screening are expected in all orders of perturbation theory.