{
  "id": "1109.4608",
  "version": "v1",
  "published": "2011-09-21T18:41:45.000Z",
  "updated": "2011-09-21T18:41:45.000Z",
  "title": "The Zak phase and the existence of edge states in graphene",
  "authors": [
    "P. Delplace",
    "D. Ullmo",
    "G. Montambaux"
  ],
  "comment": "14 pages, 19 figures",
  "journal": "Phys. Rev. B 84, 195452 (2011)",
  "doi": "10.1103/PhysRevB.84.195452",
  "categories": [
    "cond-mat.mes-hall",
    "quant-ph"
  ],
  "abstract": "We develop a method to predict the existence of edge states in graphene ribbons for a large class of boundaries. This approach is based on the bulk-edge correspondence between the quantized value of the Zak phase Z(k), which is a Berry phase across an appropriately chosen one-dimensional Brillouin zone, and the existence of a localized state of momentum k at the boundary of the ribbon. This bulk-edge correspondence is rigorously demonstrated for a one dimensional toy model as well as for graphene ribbons with zigzag edges. The range of k for which edge states exist in a graphene ribbon is then calculated for arbitrary orientations of the edges. Finally, we show that the introduction of an anisotropy leads to a topological transition in terms of the Zak phase, which modifies the localization properties at the edges. Our approach gives a new geometrical understanding of edge states, it con?firms and generalizes the results of several previous works.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2011-09-21T18:41:45.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "03.65.Vf",
      "73.22.Pr",
      "73.20.At"
    ],
    "keywords": [
      "edge states",
      "zak phase",
      "graphene ribbon",
      "bulk-edge correspondence",
      "appropriately chosen one-dimensional brillouin zone"
    ],
    "tags": [
      "journal article"
    ],
    "publication": {
      "publisher": "APS",
      "journal": "Physical Review B",
      "year": 2011,
      "month": "Nov",
      "volume": 84,
      "number": 19,
      "pages": 195452
    },
    "note": {
      "typesetting": "TeX",
      "pages": 14,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2011PhRvB..84s5452D"
    }
  }
}