{
  "id": "cond-mat/0211250",
  "version": "v1",
  "published": "2002-11-13T08:30:04.000Z",
  "updated": "2002-11-13T08:30:04.000Z",
  "title": "Duality and integer quantum Hall effect in isotropic 3D crystals",
  "authors": [
    "M. Koshino",
    "H. Aoki"
  ],
  "comment": "7 pages, 6 figures",
  "categories": [
    "cond-mat.mes-hall"
  ],
  "abstract": "We show here a series of energy gaps as in Hofstadter's butterfly, which have been shown to exist by Koshino et al [Phys. Rev. Lett. 86, 1062 (2001)] for anisotropic three-dimensional (3D) periodic systems in magnetic fields $\\Vec{B}$, also arise in the isotropic case unless $\\Vec{B}$ points in high-symmetry directions. Accompanying integer quantum Hall conductivities $(\\sigma_{xy}, \\sigma_{yz}, \\sigma_{zx})$ can, surprisingly, take values $\\propto (1,0,0), (0,1,0), (0,0,1)$ even for a fixed direction of $\\Vec{B}$ unlike in the anisotropic case. We can intuitively explain the high-magnetic field spectra and the 3D QHE in terms of quantum mechanical hopping by introducing a ``duality'', which connects the 3D system in a strong $\\Vec{B}$ with another problem in a weak magnetic field $(\\propto 1/B)$.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2002-11-13T08:30:04.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "integer quantum hall effect",
      "isotropic 3d crystals",
      "accompanying integer quantum hall conductivities",
      "weak magnetic field",
      "high-magnetic field spectra"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 7,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2002cond.mat.11250K"
    }
  }
}