The ground state of clean and defected graphene: Coulomb interactions of massless Dirac fermions, pair-distribution functions and spin-polarized phases

TL;DR

This paper investigates the applicability of the Dirac-Weyl model to graphene and defected graphene, analyzing Coulomb interactions and spin-polarized phases through first-principles calculations and correlation energy estimates.

Contribution

It demonstrates the limitations of the Dirac-Weyl model in defected graphene and assesses the stability of spin-polarized phases considering correlation effects.

Findings

Dirac-Weyl model fails for defected graphene with vacancies or N substitution.

Spin-polarized phases are suppressed in ideal graphene when correlation energies are included.

Correlation energies dominate over exchange in determining spin polarization stability.

Abstract

First-principles density functional calculations for graphene and defected graphene are used to examine when the quasi-2D electrons near the Fermi energy in graphene could be represented by massless fermions obeying a Dirac-Weyl (DW) equation. The DW model is found to be inapplicable to defected graphene containing even $\sim$3% vacancies or N substitution. However, the DW model holds in the presence of weakly adsorbed molecular layers. The possibility of spin-polarized phases (SPP) of DW-massless fermions in pure graphene is considered. The exchange energy is evaluated from the analytic pair-distribution functions as well as in $k$-space. The kinetic energy enhancement of the sipn-polarized phase nearly cancels the exchange enhancement, and the correlation energy plays a dominant residual role. The correlation energies are estimated via a model four-component 2D electron fluid whose Coulomb coupling matches that of graphene. While SPPs appear with exchange only, the inclusion of correlations suppresses them in ideal graphene.