{
  "id": "1304.7052",
  "version": "v2",
  "published": "2013-04-26T02:19:04.000Z",
  "updated": "2013-10-02T03:59:14.000Z",
  "title": "Periodic Landau gauge and Quantum Hall effect in twisted bilayer graphene",
  "authors": [
    "Yasumasa Hasegawa",
    "Mahito Kohmoto"
  ],
  "comment": "9 pages, 10 figures revised",
  "journal": "Phys. Rev. B 88, 125426 (2013)",
  "doi": "10.1103/PhysRevB.88.125426",
  "categories": [
    "cond-mat.mes-hall"
  ],
  "abstract": "Energy versus magnetic field (Hofstadter butterfly diagram) in twisted bilayer graphene is studied theoretically. If we take the usual Landau gauge, we cannot take a finite periodicity even when the magnetic flux through a supercell is a rational number. We show that the \\textit{periodic} Landau gauge, which has the periodicity in one direction, makes it possible to obtain the Hofstadter butterfly diagram. Since a supercell can be large, magnetic flux through a supercell normalized by the flux quantum can be a fractional number with a small denominator, even when a magnetic field is not extremely strong. As a result, quantized Hall conductance can be a solution of nontrivial Diophantine equation.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2013-10-02T03:59:14.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "73.22.Pr",
      "73.20.-r",
      "73.40.-c",
      "81.05.ue"
    ],
    "keywords": [
      "twisted bilayer graphene",
      "periodic landau gauge",
      "quantum hall effect",
      "hofstadter butterfly diagram",
      "magnetic field"
    ],
    "tags": [
      "journal article"
    ],
    "publication": {
      "publisher": "APS",
      "journal": "Physical Review B",
      "year": 2013,
      "month": "Sep",
      "volume": 88,
      "number": 12,
      "pages": 125426
    },
    "note": {
      "typesetting": "TeX",
      "pages": 9,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2013PhRvB..88l5426H"
    }
  }
}