{
  "id": "1410.6250",
  "version": "v1",
  "published": "2014-10-23T05:29:35.000Z",
  "updated": "2014-10-23T05:29:35.000Z",
  "title": "Survival of sharp $n=0$ Landau levels in massive tilted Dirac fermions: Protection by generalized chiral symmetry",
  "authors": [
    "Yasuhiro Hatsugai",
    "Tohru Kawarabayashi",
    "Hideo Aoki"
  ],
  "comment": "12 pages, 6 figures",
  "categories": [
    "cond-mat.mes-hall"
  ],
  "abstract": "Anomalously sharp (delta-function-like) $n=0$ Landau level in the presence of disorder is usually considered to be a manifestation of the massless Dirac fermions in magnetic fields. This property persists even when the Dirac cone is tilted, which has been shown by Kawarabayashi et al. [Phys. Rev. B {\\bf 83}, 153414 (2011)] to be a consequence of a \"generalized chiral symmetry\". Here we pose a question whether this property will be washed out when the tilted Dirac fermion becomes massive. Surprisingly, while the massive case with split $n=0$ Landau levels may seem to degrade the anomalous sharpness, the levels do remain delta-function-like. This has been shown analytically in terms of the Aharonov-Casher argument extended to the massive tilted Dirac ferimions. A key observation is that the conventional and generalized chiral operators are related with each other via a non-unitary transformation, with which the split, nonzero-energy $n=0$ wave functions of the massive system can be identified as a gauge-transformed zero-mode wave functions of the massless system. This is confirmed from a numerical result for a model tight-binding system. A message is that the chiral symmetry, rather than a simpler notion of the sublattice symmetry, is essential for the robustness of the $n=0$ Landau level, which is why the chiral symmetry remains applicable even to massive case.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2014-10-23T05:29:35.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "71.70.Di",
      "73.22.Pr"
    ],
    "keywords": [
      "landau level",
      "massive tilted dirac fermions",
      "generalized chiral symmetry",
      "protection",
      "gauge-transformed zero-mode wave functions"
    ],
    "tags": [
      "journal article"
    ],
    "publication": {
      "doi": "10.1103/PhysRevB.91.085112",
      "journal": "Physical Review B",
      "year": 2015,
      "month": "Feb",
      "volume": 91,
      "number": 8,
      "pages": "085112"
    },
    "note": {
      "typesetting": "TeX",
      "pages": 12,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "inspire": 1323502,
      "adsabs": "2015PhRvB..91h5112H"
    }
  }
}