{
  "id": "0905.2029",
  "version": "v1",
  "published": "2009-05-13T07:40:09.000Z",
  "updated": "2009-05-13T07:40:09.000Z",
  "title": "Classification of Topological Insulators and Superconductors",
  "authors": [
    "Andreas P. Schnyder",
    "Shinsei Ryu",
    "Akira Furusaki",
    "Andreas W. W. Ludwig"
  ],
  "comment": "12 pages, 5 figures; Proceedings of the L.D. Landau Memorial Conference, 2008",
  "journal": "AIP Conf. Proc. 1134, 10 (2009)",
  "categories": [
    "cond-mat.mes-hall",
    "cond-mat.str-el"
  ],
  "abstract": "An exhaustive classification scheme of topological insulators and superconductors is presented. The key property of topological insulators (superconductors) is the appearance of gapless degrees of freedom at the interface/boundary between a topologically trivial and a topologically non-trivial state. Our approach consists in reducing the problem of classifying topological insulators (superconductors) in d spatial dimensions to the problem of Anderson localization at a (d-1) dimensional boundary of the system. We find that in each spatial dimension there are precisely five distinct classes of topological insulators (superconductors). The different topological sectors within a given topological insulator (superconductor) can be labeled by an integer winding number or a Z_2 quantity. One of the five topological insulators is the 'quantum spin Hall' (or: Z_2 topological) insulator in d=2, and its generalization in d=3 dimensions. For each dimension d, the five topological insulators correspond to a certain subset of five of the ten generic symmetry classes of Hamiltonians introduced more than a decade ago by Altland and Zirnbauer in the context of disordered systems (which generalizes the three well known \"Wigner-Dyson'' symmetry classes).",
  "revisions": [
    {
      "version": "v1",
      "updated": "2009-05-13T07:40:09.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "61.43.Dq",
      "72.15.Rn",
      "64.60.-i",
      "73.43.Nq"
    ],
    "keywords": [
      "superconductor",
      "spatial dimension",
      "quantum spin hall",
      "generic symmetry classes",
      "exhaustive classification scheme"
    ],
    "tags": [
      "conference paper",
      "journal article"
    ],
    "publication": {
      "publisher": "AIP",
      "journal": "AIP Conf. Proc."
    },
    "note": {
      "typesetting": "TeX",
      "pages": 12,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2009AIPC.1134...10S"
    }
  }
}