{
  "id": "1501.02874",
  "version": "v1",
  "published": "2015-01-13T03:09:00.000Z",
  "updated": "2015-01-13T03:09:00.000Z",
  "title": "Notes on topological insulators",
  "authors": [
    "Dan Li",
    "Ralph M. Kaufmann",
    "Birgit Wehefritz-Kaufmann"
  ],
  "comment": "47 pages",
  "categories": [
    "math-ph",
    "math.MP"
  ],
  "abstract": "This paper is a survey of the $\\mathbb{Z}/\\mathbb{Z}_2$-valued invariants of topological insulators in condensed matter physics. The $\\mathbb{Z}$-valued topological invariant was originally called the TKNN invariant in physics, which has been fully understood as the first Chern number. The $\\mathbb{Z}_2$ invariant is more mysterious, we will devote our efforts to reviewing its equivalent descriptions from different point of views. We emphasize that both invariants are realizations of the Atiyah--Singer index theorem in condensed matter physics. The topological K-theory also plays an important role in the classification of topological insulators with different symmetries.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2015-01-13T03:09:00.000Z"
    }
  ],
  "analyses": {
    "themes": [
      {
        "category": "cond-mat.mes-hall",
        "topics": [
          "topological insulator"
        ]
      }
    ],
    "keywords": [
      "topological insulators",
      "quantum Hall effect",
      "condensed matter physics",
      "topological invariant",
      "Atiyah-Singer index theorem",
      "K-theory classification"
    ],
    "tags": [
      "review article"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 47,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "inspire": 1338647,
      "adsabs": "2015arXiv150102874K"
    }
  }
}