The importance of sigma bonding electrons for the accurate description of electron correlation in graphene

TL;DR

This paper investigates how sigma bonding electrons influence electron correlation in graphene, revealing their significant role in screening and the material's weakly correlated semimetal behavior.

Contribution

It demonstrates that sigma electrons contribute substantially to electron structure factors at relevant energies and distances, clarifying the screening mechanism in graphene.

Findings

Sigma electrons significantly affect structure factors up to 80 Å.

Graphene's weak correlation arises from Coulomb interactions involving sigma electrons.

Ab-initio calculations show strong sigma electron contribution at experimental energies.

Abstract

Electron correlation in graphene is unique because of the interplay of the Dirac cone dispersion of $\pi$ electrons with long range Coulomb interaction. The random phase approximation predicts no metallic screening at long distance and low energy because of the zero density of states at Fermi level, so one might expect that graphene should be a poorly screened system. However, empirically graphene is a weakly interacting semimetal, which leads to the question of how electron correlations take place in graphene at different length scales. We address this question by computing the equal time and dynamic structure factor $S(\vec q)$ and $S(\vec q, \omega)$ of freestanding graphene using {\it ab-initio} fixed-node diffusion Monte Carlo and the random phase approximation. We find that the $\sigma$ electrons contribute strongly to $S(\vec q,\omega)$ for relevant experimental values of $\omega$ even at distances up to around 80 \AA. These findings illustrate how the emergent physics from underlying Coulomb interactions results in the observed weakly correlated semimetal.