{
  "id": "1104.5632",
  "version": "v3",
  "published": "2011-04-29T14:07:14.000Z",
  "updated": "2011-08-17T13:44:08.000Z",
  "title": "Klein tunneling in graphene: optics with massless electrons",
  "authors": [
    "P. E. Allain",
    "J. N. Fuchs"
  ],
  "comment": "short review article, 18 pages, 14 figures; v3: references added, several figures slightly modified",
  "journal": "Eur. Phys. J. B 83, 301-317 (2011)",
  "doi": "10.1140/epjb/e2011-20351-3",
  "categories": [
    "cond-mat.mes-hall",
    "quant-ph"
  ],
  "abstract": "This article provides a pedagogical review on Klein tunneling in graphene, i.e. the peculiar tunneling properties of two-dimensional massless Dirac electrons. We consider two simple situations in detail: a massless Dirac electron incident either on a potential step or on a potential barrier and use elementary quantum wave mechanics to obtain the transmission probability. We emphasize the connection to related phenomena in optics, such as the Snell-Descartes law of refraction, total internal reflection, Fabry-P\\'erot resonances, negative refraction index materials (the so called meta-materials), etc. We also stress that Klein tunneling is not a genuine quantum tunneling effect as it does not necessarily involve passing through a classically forbidden region via evanescent waves. A crucial role in Klein tunneling is played by the conservation of (sublattice) pseudo-spin, which is discussed in detail. A major consequence is the absence of backscattering at normal incidence, of which we give a new shorten proof. The current experimental status is also thoroughly reviewed. The appendix contains the discussion of a one-dimensional toy model that clearly illustrates the difference in Klein tunneling between mono- and bi-layer graphene.",
  "revisions": [
    {
      "version": "v3",
      "updated": "2011-08-17T13:44:08.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "klein tunneling",
      "massless electrons",
      "elementary quantum wave mechanics",
      "one-dimensional toy model",
      "current experimental status"
    ],
    "tags": [
      "review article",
      "journal article"
    ],
    "publication": {
      "journal": "European Physical Journal B",
      "year": 2011,
      "month": "Oct",
      "volume": 83,
      "number": 3,
      "pages": 301
    },
    "note": {
      "typesetting": "TeX",
      "pages": 18,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "inspire": 924308,
      "adsabs": "2011EPJB...83..301A"
    }
  }
}