{
  "id": "0907.5253",
  "version": "v1",
  "published": "2009-07-30T04:22:34.000Z",
  "updated": "2009-07-30T04:22:34.000Z",
  "title": "Fundamental relation between longitudinal and transverse conductivities in the quantum Hall system",
  "authors": [
    "Akira Endo",
    "Naomichi Hatano",
    "Hiroaki Nakamura",
    "Ryoen Shirasaki"
  ],
  "comment": "21 pages, 8 figures, accepted for publication in J. Phys.: Condens. Matter",
  "journal": "J. Phys.: Condens. Matter 21 (2009) 345803",
  "doi": "10.1088/0953-8984/21/34/345803",
  "categories": [
    "cond-mat.mes-hall"
  ],
  "abstract": "We investigate the relation between the diagonal ($\\sigma_{xx}$) and off-diagonal ($\\sigma_{xy}$) components of the conductivity tensor in the quantum Hall system. We calculate the conductivity components for a short-range impurity potential using the linear response theory, employing an approximation that simply replaces the self-energy by a constant value $-i \\hbar /(2 \\tau)$ with $\\tau$ the scattering time. The approximation is equivalent to assuming that the broadening of a Landau level due to disorder is represented by a Lorentzian with the width $\\Gamma = \\hbar /(2 \\tau)$. Analytic formulas are obtained for both $\\sigma_{xx}$ and $\\sigma_{xy}$ within the framework of this simple approximation at low temperatures. By examining the leading terms in $\\sigma_{xx}$ and $\\sigma_{xy}$, we find a proportional relation between $\\mathrm{d}\\sigma_{xy}/\\mathrm{d}B$ and $B \\sigma_{xx}^2$. The relation, after slight modification to account for the long-range nature of the impurity potential, is shown to be in quantitative agreement with experimental results obtained in the GaAs/AlGaAs two-dimensional electron system at the low magnetic-field regime where spin splitting is negligibly small.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2009-07-30T04:22:34.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "quantum hall system",
      "transverse conductivities",
      "fundamental relation",
      "longitudinal",
      "gaas/algaas two-dimensional electron system"
    ],
    "tags": [
      "journal article"
    ],
    "publication": {
      "journal": "Journal of Physics Condensed Matter",
      "year": 2009,
      "month": "Aug",
      "volume": 21,
      "number": 34,
      "pages": 345803
    },
    "note": {
      "typesetting": "TeX",
      "pages": 21,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2009JPCM...21H5803E"
    }
  }
}