{
  "id": "cond-mat/9811112",
  "version": "v3",
  "published": "1998-11-09T07:31:16.000Z",
  "updated": "1999-12-27T06:56:59.000Z",
  "title": "Insensitivity of Quantized Hall Conductance to Disorder and Interactions",
  "authors": [
    "Tohru Koma"
  ],
  "comment": "LaTeX, 62 pages, no figures, typos corrected, some references added, discussion on the standard time-dependent vector potential added, accepted for publication in J. Stat. Phys",
  "categories": [
    "cond-mat.mes-hall",
    "cond-mat.stat-mech"
  ],
  "abstract": "A two-dimensional quantum Hall system is studied for a wide class of potentials including single-body random potentials and repulsive electron-electron interactions. We assume that there exists a non-zero excitation gap above the ground state(s), and then the conductance is derived from the linear perturbation theory with a sufficiently weak electric field. Under these two assumptions, we proved that the Hall conductance $\\sigma_{xy}$ and the diagonal conductance $\\sigma_{yy}$ satisfy $|\\sigma_{xy}+e^2\\nu/h|\\le{\\rm const.}L^{-1/12}$ and $|\\sigma_{yy}|\\le{\\rm const.}L^{-1/12}$. Here $e^2/h$ is the universal conductance with the charge $-e$ of electron and the Planck constant $h$; $\\nu$ is the filling factor of the Landau level, and $L$ is the linear dimension of the system. In the thermodymanic limit, our results show $\\sigma_{xy}=-e^2\\nu/h$ and $\\sigma_{yy}=0$. The former implies that integral and fractional filling factors $\\nu$ with a gap lead to, respectively, integral and fractional quantizations of the Hall conductance.",
  "revisions": [
    {
      "version": "v3",
      "updated": "1999-12-27T06:56:59.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "quantized hall conductance",
      "interactions",
      "insensitivity",
      "two-dimensional quantum hall system",
      "sufficiently weak electric field"
    ],
    "note": {
      "typesetting": "LaTeX",
      "pages": 62,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "1998cond.mat.11112K"
    }
  }
}