{
  "id": "cond-mat/0506581",
  "version": "v2",
  "published": "2005-06-22T19:17:46.000Z",
  "updated": "2005-06-27T18:43:47.000Z",
  "title": "$Z_2$ Topological Order and the Quantum Spin Hall Effect",
  "authors": [
    "C. L. Kane",
    "E. J. Mele"
  ],
  "comment": "4 pages RevTeX. Added reference, minor corrections",
  "journal": "Phys. Rev. Lett. 95, 146802 (2005)",
  "doi": "10.1103/PhysRevLett.95.146802",
  "categories": [
    "cond-mat.mes-hall"
  ],
  "abstract": "The quantum spin Hall (QSH) phase is a time reversal invariant electronic state with a bulk electronic band gap that supports the transport of charge and spin in gapless edge states. We show that this phase is associated with a novel $Z_2$ topological invariant, which distinguishes it from an ordinary insulator. The $Z_2$ classification, which is defined for time reversal invariant Hamiltonians, is analogous to the Chern number classification of the quantum Hall effect. We establish the $Z_2$ order of the QSH phase in the two band model of graphene and propose a generalization of the formalism applicable to multi band and interacting systems.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2005-06-27T18:43:47.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "73.61.Wp",
      "72.25.Hg",
      "85.75.-d",
      "73.43.-f"
    ],
    "keywords": [
      "quantum spin hall effect",
      "topological order",
      "time reversal invariant electronic state",
      "bulk electronic band gap",
      "time reversal invariant hamiltonians"
    ],
    "tags": [
      "journal article",
      "famous paper"
    ],
    "publication": {
      "publisher": "APS",
      "journal": "Phys. Rev. Lett."
    },
    "note": {
      "typesetting": "RevTeX",
      "pages": 4,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "inspire": 707562
    }
  }
}