{
  "id": "cond-mat/0701431",
  "version": "v1",
  "published": "2007-01-18T07:49:53.000Z",
  "updated": "2007-01-18T07:49:53.000Z",
  "title": "Topological aspects of graphene: Dirac fermions and the bulk-edge correspondence in magnetic fields",
  "authors": [
    "Y. Hatsugai",
    "T. Fukui",
    "H. Aoki"
  ],
  "comment": "8 pages, 5 figures, proceeding of the graphene conference at MPIPKS Dresden, Sep. 25-Oct.1, 2006",
  "doi": "10.1140/epjst/e2007-00233-5",
  "categories": [
    "cond-mat.mes-hall"
  ],
  "abstract": "We discuss topological aspects of electronic properties of graphene, including edge effects, with the tight-binding model on a honeycomb lattice and its extensions to show the following: (i) Appearance of the pairn of massless Dirac dispersions, which is the origin of anomalous properties including a peculiar quantum Hall effect (QHE), is not accidental to honeycomb, but is rather generic for a class of two-dimensional lattices that interpolate between square and $\\pi$-flux lattices. Persistence of the peculiar QHE is interpreted as a topological stability. (ii) While we have the massless Dirac dispersion only around E=0, the anomalous QHE associated with the Dirac cone unexpectedly persists for a wide range of the chemical potential. The range is bounded by van Hove singularities, at which we predict a transition to the ordinary fermion behavior acompanied by huge jumps in the QHE with a sign change. (iii) For edges we establish a coincidence between the quantum Hall effect in the bulk and the quantum Hall effect for the edge states, which is a manifestation of the topological bulk-edge correspondence. We have also explicitly shown that the E=0 edge states in honeycomb in zero magnetic field persist in magnetic field.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2007-01-18T07:49:53.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "bulk-edge correspondence",
      "topological aspects",
      "dirac fermions",
      "massless dirac dispersion",
      "edge states"
    ],
    "tags": [
      "conference paper",
      "journal article"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 8,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}