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

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.

arXiv comment~7 pages, 6 figures

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• Effect of Uniaxial Strain on Ferromagnetic Instability and Formation of Localized Magnetic States on Adatoms in Graphene
• Electronic structure and the minimum conductance of a graphene layer on SiO2 from density-functional methods.
• Transition of Graphene on a Substrate to a Semimetallic State
• Electron Correlations in Bilayer Graphene