{
  "id": "1609.07096",
  "version": "v1",
  "published": "2016-09-22T18:18:26.000Z",
  "updated": "2016-09-22T18:18:26.000Z",
  "title": "Scale-invariant puddles in Graphene: Geometric properties of electron-hole distribution at the Dirac point",
  "authors": [
    "M. N. Najafi",
    "M. Ghasemi Nezhadhaghighi"
  ],
  "comment": "12 pages, 10 figures",
  "categories": [
    "cond-mat.mes-hall",
    "cond-mat.stat-mech"
  ],
  "abstract": "We characterize the carrier density profile of the ground state of graphene in the presence of particle-particle interaction and random charged impurity for zero gate voltage. We provide detailed analysis on the resulting spatially inhomogeneous electron gas taking into account the particle-particle interaction and the remote coulomb disorder on an equal footing within the Thomas-Fermi-Dirac theory. We present some general features of the carrier density probability measure of the graphene sheet. We also show that, when viewed as a random surface, the resulting electron-hole puddles at zero chemical potential show peculiar self-similar statistical properties. Although the disorder potential is chosen to be Gaussian, we show that the charge field is non-Gaussian with unusual Kondev relations which can be regarded as a new class of two-dimensional (2D) random-field surfaces.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2016-09-22T18:18:26.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "dirac point",
      "geometric properties",
      "electron-hole distribution",
      "scale-invariant puddles",
      "spatially inhomogeneous electron gas"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 12,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}