{
  "id": "1709.01929",
  "version": "v1",
  "published": "2017-09-06T18:00:02.000Z",
  "updated": "2017-09-06T18:00:02.000Z",
  "title": "Rotation Anomaly and Topological Crystalline Insulators",
  "authors": [
    "Chen Fang",
    "Liang Fu"
  ],
  "comment": "4+6 pages, 3+2 figures and 1 table",
  "categories": [
    "cond-mat.mes-hall",
    "hep-th"
  ],
  "abstract": "We show that in the presence of $n$-fold rotation symmetries and time-reversal symmetry, the number of fermion flavors must be a multiple of $2n$ ($n=2,3,4,6$) on two-dimensional lattices, a stronger version of the well-known fermion doubling theorem in the presence of only time-reversal symmetry. The violation of the multiplication theorems indicates anomalies, and may only occur on the surface of new classes of topological crystalline insulators. Put on a cylinder, these states have $n$ Dirac cones on the top and on the bottom surfaces, connected by $n$ helical edge modes on the side surface.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2017-09-06T18:00:02.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "topological crystalline insulators",
      "rotation anomaly",
      "time-reversal symmetry",
      "fold rotation symmetries",
      "well-known fermion doubling theorem"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 6,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}