We discuss the validity (or not) of the ring-diagram approximation (i.e. RPA) in the calculation of graphene self-energy in the weak-coupling (rs≪1) limit, showing that RPA is a controlled and valid approximation for \textit{extrinsic} graphene where the Fermi level is away from the Dirac point.
Cite
@article{arxiv.0708.3239,
title = {Electron-Electron Interactions in Graphene},
author = {S. Das Sarma and Ben Yu-Kuang Hu and E. H. Hwang and Wang-Kong Tse},
journal= {arXiv preprint arXiv:0708.3239},
year = {2007}
}