▎ 摘　　要

First-principles density-functional calculations for graphene and defective graphene are used to examine when the quasi-two-dimensional 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 defective graphene containing even similar to 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 two-dimensional electron fluid whose Coulomb coupling matches that of graphene. While SPPs appear with exchange only, the inclusion of correlations suppresses them in ideal graphene.