Spin-Density Localization in Graphene at Boundaries and at Vacancy Defects

The degree of localization of nonbonding orbitals (and the related spin density) in defected or decorated graphenic materials is addressed. For a defect consisting of a translationally symmetric boundary, such orbitals (if they occur) appear to be exponentially localized at the boundary, with the range correlating with the "mobility gap" at the corresponding wave vector. For a defect consisting of vacancies of one or more nearby sites, such orbitals (if they occur) appear to be localized around the defect with a power-law decay away from the defect. Moreover, a simple criterion for such defect-localized orbitals, as well as some characteristics and possible consequences of the nonbonding defect-localized orbitals, is noted.