{
  "id": "1605.03469",
  "version": "v1",
  "published": "2016-05-11T15:12:02.000Z",
  "updated": "2016-05-11T15:12:02.000Z",
  "title": "Coulomb charging energy of vacancy-induced states in graphene",
  "authors": [
    "Miranda G. Vladimir",
    "Luis G. G. V. Dias da Silva",
    "Caio H. Lewenkopf"
  ],
  "comment": "13 pages, 9 figures",
  "categories": [
    "cond-mat.mes-hall"
  ],
  "abstract": "Vacancies in graphene have been proposed to give rise to $\\pi$-like magnetism in carbon materials, a conjecture which has been supported by recent experimental evidence. A key element in this \"vacancy magnetism\" is the formation of magnetic moments in vacancy-induced electronic states. In this work we compute the charging energy $U$ of a single-vacancy generated localized state for bulk graphene and graphene ribbons. We use a tight-binding model to calculate the dependency of the charging energy $U$ on the amplitudes of the localized wave function on the graphene lattice sites. We show that for bulk graphene $U$ scales with the system size $L$ as $(\\ln L)^{-2}$, confirming the predictions in the literature, based on heuristic arguments. In contrast, we find that for realistic system sizes $U$ is of the order of eV, a value that is orders of magnitude higher than the previously reported estimates. Finally, when edges are considered, we show that $U$ is very sensitive to the vacancy position with respect to the graphene flake boundaries. In the case of armchair nanoribbons, we find a strong enhancement of $U$ in certain vacancy positions as compared to the value for vacancies in bulk graphene.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2016-05-11T15:12:02.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "coulomb charging energy",
      "vacancy-induced states",
      "bulk graphene",
      "vacancy position",
      "graphene lattice sites"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 13,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}