{
  "id": "0806.0573",
  "version": "v1",
  "published": "2008-06-03T16:09:54.000Z",
  "updated": "2008-06-03T16:09:54.000Z",
  "title": "Skyrme and Wigner crystals in graphene",
  "authors": [
    "R. Cote",
    "J. -F. Jobidon",
    "H. A. Fertig"
  ],
  "comment": "14 pages with 11 figures",
  "journal": "Phys. Rev. B 78, 085309 (2008).",
  "doi": "10.1103/PhysRevB.78.085309",
  "categories": [
    "cond-mat.mes-hall"
  ],
  "abstract": "At low-energy, the band structure of graphene can be approximated by two degenerate valleys $(K,K^{\\prime})$ about which the electronic spectra of the valence and conduction bands have linear dispersion relations. An electronic state in this band spectrum is a linear superposition of states from the $A$ and $B$ sublattices of the honeycomb lattice of graphene. In a quantizing magnetic field, the band spectrum is split into Landau levels with level N=0 having zero weight on the $B(A)$ sublattice for the $% K(K^{\\prime})$ valley. Treating the valley index as a pseudospin and assuming the real spins to be fully polarized, we compute the energy of Wigner and Skyrme crystals in the Hartree-Fock approximation. We show that Skyrme crystals have lower energy than Wigner crystals \\textit{i.e.} crystals with no pseudospin texture in some range of filling factor $\\nu $ around integer fillings. The collective mode spectrum of the valley-skyrmion crystal has three linearly-dispersing Goldstone modes in addition to the usual phonon mode while a Wigner crystal has only one extra Goldstone mode with a quadratic dispersion. We comment on how these modes should be affected by disorder and how, in principle, a microwave absorption experiment could distinguish between Wigner and Skyrme crystals.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2008-06-03T16:09:54.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "73.20.Qt",
      "73.21.-b",
      "73.22.Lp"
    ],
    "keywords": [
      "wigner crystal",
      "skyrme crystals",
      "band spectrum",
      "extra goldstone mode",
      "linear dispersion relations"
    ],
    "tags": [
      "journal article"
    ],
    "publication": {
      "publisher": "APS",
      "journal": "Physical Review B",
      "year": 2008,
      "month": "Aug",
      "volume": 78,
      "number": 8,
      "pages": "085309"
    },
    "note": {
      "typesetting": "TeX",
      "pages": 14,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2008PhRvB..78h5309C"
    }
  }
}