{
  "id": "1403.5984",
  "version": "v2",
  "published": "2014-03-24T14:55:11.000Z",
  "updated": "2014-07-31T18:49:06.000Z",
  "title": "On the Role of Symmetries in the Theory of Photonic Crystals",
  "authors": [
    "Giuseppe De Nittis",
    "Max Lein"
  ],
  "comment": "34 pages, 2 figures",
  "categories": [
    "cond-mat.mes-hall",
    "math-ph",
    "math.MP",
    "physics.optics"
  ],
  "abstract": "We discuss the role of the symmetries in photonic crystals and classify them according to the Cartan-Altland-Zirnbauer scheme. Of particular importance are complex conjugation C and time-reversal T, but we identify also other significant symmetries. Borrowing the jargon of the classification theory of topological insulators, we show that C is a particle-hole-type symmetry rather than a time-reversal symmetry if one consider the Maxwell operator in the first-order formalism where the dynamical Maxwell equations can be rewritten as a Schr\\\"odinger equation; The symmetry which implements physical time-reversal is a chiral-type symmetry. We justify by an analysis of the band structure why the first-order formalism seems to be more advantageous than the second-order formalism. Moreover, based on the Schr\\\"odinger formalism, we introduce a class of effective (tight-binding) models called Maxwell-Harper operators. Some considerations about the breaking of the particle-hole-type symmetry in the case of gyrotropic crystals are added at the end of this paper.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2014-07-31T18:49:06.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "photonic crystals",
      "first-order formalism",
      "particle-hole-type symmetry",
      "cartan-altland-zirnbauer scheme",
      "significant symmetries"
    ],
    "tags": [
      "journal article"
    ],
    "publication": {
      "doi": "10.1016/j.aop.2014.07.032",
      "journal": "Annals of Physics",
      "year": 2014,
      "month": "Nov",
      "volume": 350,
      "pages": 568
    },
    "note": {
      "typesetting": "TeX",
      "pages": 34,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2014AnPhy.350..568D"
    }
  }
}