{
  "id": "1607.05904",
  "version": "v1",
  "published": "2016-07-20T10:33:29.000Z",
  "updated": "2016-07-20T10:33:29.000Z",
  "title": "Electron dynamics in graphene with spin-orbit couplings and periodic potentials",
  "authors": [
    "Ranjani Seshadri",
    "Diptiman Sen"
  ],
  "comment": "11 pages, 10 figures",
  "categories": [
    "cond-mat.mes-hall"
  ],
  "abstract": "We use both lattice and continuum models to study the energy-momentum dispersion and the dynamics of a wave packet for an electron moving in graphene in the presence of spin-orbit couplings and either a single potential barrier or a periodic array of potential barriers. Both Kane-Mele and Rashba spin-orbit couplings are considered. In the presence of a single potential barrier, we show that there are states localized along the barrier. When the Kane-Mele and Rashba couplings are equal in magnitude, we find that the dispersion consists of both massless Dirac and massive Dirac states. The two kinds of states respond differently to a potential barrier; the massless states Klein tunnel through the barrier at normal incidence while the massive states reflect from it. A periodic potential is known to generate additional Dirac points; we show that spin-orbit couplings generally open gaps at those points. Finally, we study the time evolution of a wave packet in the presence of a periodic potential. We discover special points in momentum space where there is almost no spreading of a wave packet; there are six such points in graphene when the spin-orbit couplings are absent.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2016-07-20T10:33:29.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "periodic potential",
      "electron dynamics",
      "wave packet",
      "single potential barrier",
      "generate additional dirac points"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 11,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}