{
  "id": "1804.00781",
  "version": "v1",
  "published": "2018-04-03T01:52:48.000Z",
  "updated": "2018-04-03T01:52:48.000Z",
  "title": "Winding vector: how to annihilate two Dirac points with the same charge",
  "authors": [
    "Gilles Montambaux",
    "Lih-King Lim",
    "Jean-Noël Fuchs",
    "Frédéric Piéchon"
  ],
  "comment": "5 pages, 6 figures",
  "journal": "Phys. Rev. Lett. 121, 256402 (2018)",
  "doi": "10.1103/PhysRevLett.121.256402",
  "categories": [
    "cond-mat.mes-hall"
  ],
  "abstract": "The merging or emergence of a pair of Dirac points may be classified according to whether the winding numbers which characterize them are opposite ($+-$ scenario) or identical ($++$ scenario). From the touching point between two parabolic bands (one of them can be flat), two Dirac points with the {\\it same} winding number emerge under appropriate distortion (interaction, etc), following the $++$ scenario. Under further distortion, these Dirac points merge following the $+-$ scenario, that is corresponding to {\\it opposite} winding numbers. This apparent contradiction is solved by the fact that the winding number is actually defined around a unit vector on the Bloch sphere and that this vector rotates during the motion of the Dirac points. This is shown here within the simplest two-band lattice model (Mielke) exhibiting a flat band. We argue on several examples that the evolution between the two scenarios is general.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2018-04-03T01:52:48.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "winding number",
      "winding vector",
      "annihilate",
      "simplest two-band lattice model",
      "dirac points merge"
    ],
    "tags": [
      "journal article"
    ],
    "publication": {
      "publisher": "APS",
      "journal": "Phys. Rev. Lett."
    },
    "note": {
      "typesetting": "TeX",
      "pages": 5,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}