Effects of short-range electron-electron interactions in doped graphene

TL;DR

This paper investigates how short-range electron-electron interactions influence the electronic properties of doped graphene with impurities, revealing enhanced impurity state resonance and interaction-dependent energy gap modifications.

Contribution

It provides a detailed theoretical analysis of interaction effects on impurity states in doped graphene using a self-consistent Hubbard model approach.

Findings

Interactions enhance impurity state resonance near the Fermi level.

Energy gap size at high-symmetry points is significantly affected by interactions.

Supercell geometry subtly influences the interaction effects.

Abstract

We study theoretically the effects of short-range electron-electron interactions on the electronic structure of graphene, in the presence of single substitutional impurities. Our computational approach is based on the $\pi$ orbital tight-binding approximation for graphene, with the electron-electron interactions treated self-consistently at the level of the mean-field Hubbard model. We compare explicitly non-interacting and interacting cases with varying interaction strength and impurity potential strength. We focus in particular on the interaction-induced modifications in the local density of states around the impurity, which is a quantity that can be directly probed by scanning tunneling spectroscopy of doped graphene. We find that the resonant character of the impurity states near the Fermi level is enhanced by the interactions. Furthermore, the size of the energy gap, which opens at high-symmetry points of the Brillouin zone of the supercell upon doping, is significantly affected by the interactions. The details of this effect depend subtly on the supercell geometry. We use a perturbative model to explain these features and find quantitative agreement with numerical results.