{
  "id": "1711.04688",
  "version": "v1",
  "published": "2017-11-13T16:32:27.000Z",
  "updated": "2017-11-13T16:32:27.000Z",
  "title": "Integer quantum Hall transition in a $\\textit{fraction}$ of a Landau level",
  "authors": [
    "Matteo Ippoliti",
    "Scott D. Geraedts",
    "R. N. Bhatt"
  ],
  "comment": "11 pages (including appendix and references), 7 figures",
  "categories": [
    "cond-mat.dis-nn",
    "cond-mat.mes-hall",
    "quant-ph"
  ],
  "abstract": "We investigate the quantum Hall problem in the lowest Landau level in two dimensions, in the presence of an arbitrary number of $\\delta$-function potentials arranged in different geometric configurations. When the number of delta functions $N_\\delta$ is smaller than the number of flux quanta through the system ($N_\\phi$), there is a manifold of $(N_\\phi-N_\\delta)$ degenerate states at the original Landau level energy. We prove that the total Chern number of this set of states is +1 regardless of the number or position of the $\\delta$ functions. Furthermore, we find numerically that, upon the addition of disorder, this subspace includes a quantum Hall transition which is (in a well-defined sense) $\\textit{quantitatively}$ the same as that for the lowest Landau level without $\\delta$-function impurities, but with a reduced number $N_\\phi' \\equiv N_\\phi-N_\\delta$ of magnetic flux quanta. We discuss the implications of these results for studies of the integer plateau transitions, as well as for the many-body problem in the presence of electron-electron interactions.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2017-11-13T16:32:27.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "integer quantum hall transition",
      "lowest landau level",
      "original landau level energy",
      "quantum hall problem",
      "magnetic flux quanta"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 11,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}