{
  "id": "0810.4920",
  "version": "v2",
  "published": "2008-10-27T21:16:23.000Z",
  "updated": "2009-05-13T16:36:32.000Z",
  "title": "Quantum site percolation on triangular lattice and the integer quantum Hall effect",
  "authors": [
    "V. V. Mkhitaryan",
    "M. E. Raikh"
  ],
  "comment": "10 pages, 8 figures; published version",
  "journal": "Phys. Rev. B 79, 125401 (2009)",
  "doi": "10.1103/PhysRevB.79.125401",
  "categories": [
    "cond-mat.mes-hall"
  ],
  "abstract": "Generic classical electron motion in a strong perpendicular magnetic field and random potential reduces to the bond percolation on a square lattice. Here we point out that for certain smooth 2D potentials with 120 degrees rotational symmetry this problem reduces to the site percolation on a triangular lattice. We use this observation to develop an approximate analytical description of the integer quantum Hall transition. For this purpose we devise a quantum generalization of the real-space renormalization group (RG) treatment of the site percolation on the triangular lattice. In quantum case, the RG transformation describes the evolution of the distribution of the $3\\times 3$ scattering matrix at the sites. We find the fixed point of this distribution and use it to determine the critical exponent, $\\nu$, for which we find the value $\\nu \\approx 2.3-2.76$. The RG step involves only a single Hikami box, and thus can serve as a minimal RG description of the quantum Hall transition.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2009-05-13T16:36:32.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "72.15.Rn",
      "73.20.Fz",
      "73.43.-f"
    ],
    "keywords": [
      "integer quantum hall effect",
      "triangular lattice",
      "quantum site percolation",
      "integer quantum hall transition",
      "strong perpendicular magnetic field"
    ],
    "tags": [
      "journal article"
    ],
    "publication": {
      "publisher": "APS",
      "journal": "Physical Review B",
      "year": 2009,
      "month": "Mar",
      "volume": 79,
      "number": 12,
      "pages": 125401
    },
    "note": {
      "typesetting": "TeX",
      "pages": 10,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2009PhRvB..79l5401M"
    }
  }
}