{
  "id": "0907.0500",
  "version": "v1",
  "published": "2009-07-02T23:12:48.000Z",
  "updated": "2009-07-02T23:12:48.000Z",
  "title": "A universal Hamiltonian for the motion and the merging of Dirac cones in a two-dimensional crystal",
  "authors": [
    "G. Montambaux",
    "F. Piechon",
    "J. -N. Fuchs",
    "M. O. Goerbig"
  ],
  "comment": "18 pages, 15 figures",
  "journal": "Eur. Phys. J. B 72, 509 (2009)",
  "categories": [
    "cond-mat.mes-hall"
  ],
  "abstract": "We propose a simple Hamiltonian to describe the motion and the merging of Dirac points in the electronic spectrum of two-dimensional electrons. This merging is a topological transition which separates a semi-metallic phase with two Dirac cones from an insulating phase with a gap. We calculate the density of states and the specific heat. The spectrum in a magnetic field B is related to the resolution of a Schrodinger equation in a double well potential. They obey the general scaling law e_n \\propto B^{2/3} f_n(Delta /B^{2/3}. They evolve continuously from a sqrt{n B} to a linear (n+1/2)B dependence, with a [(n+1/2)B]^{2/3} dependence at the transition. The spectrum in the vicinity of the topological transition is very well described by a semiclassical quantization rule. This model describes continuously the coupling between valleys associated with the two Dirac points, when approaching the transition. It is applied to the tight-binding model of graphene and its generalization when one hopping parameter is varied. It remarkably reproduces the low field part of the Rammal-Hofstadter spectrum for the honeycomb lattice.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2009-07-02T23:12:48.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "71.70.Di",
      "81.05.Uw",
      "67.85.-d"
    ],
    "keywords": [
      "dirac cones",
      "two-dimensional crystal",
      "universal hamiltonian",
      "dirac points",
      "topological transition"
    ],
    "tags": [
      "journal article"
    ],
    "publication": {
      "doi": "10.1140/epjb/e2009-00383-0",
      "journal": "European Physical Journal B",
      "year": 2009,
      "month": "Dec",
      "volume": 72,
      "number": 4,
      "pages": 509
    },
    "note": {
      "typesetting": "TeX",
      "pages": 18,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2009EPJB...72..509M"
    }
  }
}