Abstract— We employ the Green’s functiontechnique to investigate the vacancy-induced quasi-localized magnetic momentformation in monolayer graphene starting with the Dirac Hamiltonian, whichfocuses on the π- orbitals only, involving the nearest neighbor(NN)(t) andmoderate second neighbor(SN)(t′ < t/3) hopping integrals. The vacancy defect is modeled by the addition ofthe on-site perturbation potential to the Hamiltonian. We find that, when (t′/t) << 1, the vacancy induced π-state atthe zero of energy(zero-mode state(ZMS)) does not inhabit the minoritysub-lattice due to the strong scalar potential induced by the vacancy(the ZMSsget lodged in the majority sub-lattice) whereas, when (t′/t) is increased, the ZMS is somewhat suppressed. This shows that, not only the shift of theFermi energy away from the linearly-dispersive Dirac points, the issue of thistopological localization is also hinged on the ratio (t′/t). Furthermore, when a vacancy is present, thethree sp2- hybridized σ states of each of the three nearest-neighborcarbon atoms, forming a carbon triangle surrounding the vacancy, are close tothe Fermi energy (EF). TheHund’s coupling between these σ electrons and the remaining electron whichoccupies the π state spin polarizes the π state leading to local momentformation close to EF. Since the system at the Fermi level has lowelectronic density, there is poor screening of such magnetic moments. This maylead to a high Curie temperature for such vacancy-induced moments.
Keywords: Green’s function , sp2- hybridized σ states, Vacancy defect, Hund’scoupling, Spin polarized π- state, Quasi-localized magnetic moment.
PACS: 81.05 ue