{
  "id": "1810.01908",
  "version": "v1",
  "published": "2018-10-03T18:38:43.000Z",
  "updated": "2018-10-03T18:38:43.000Z",
  "title": "Landau quantization of nearly degenerate bands",
  "authors": [
    "Chong Wang",
    "Wenhui Duan",
    "Leonid Glazman",
    "A. Alexandradinata"
  ],
  "comment": "23 pages, 8 figures",
  "categories": [
    "cond-mat.mes-hall"
  ],
  "abstract": "In the semiclassical theory of Landau levels, a Bloch electron is driven by a magnetic field along constant-energy band contours known as cyclotron orbits. We introduce a quantization rule for Landau levels of nearly-degenerate orbits whose differential area ($\\delta S$) in $\\boldsymbol{k}$-space is much smaller than their average area $S$. The splitting of two nearly-degenerate orbits commonly originates from spin-orbit coupling, or from the breaking of a crystalline point-group symmetry. By treating both $\\delta S/S$ and $1/l^2S$ ($l$ being the magnetic length) as small parameters with finite ratio $l^2\\delta S$, our perspective diverges from and generalizes previous semiclassical theories. $1/l^2\\delta S$ measures the hybridization of split orbits due to the Zeeman interaction; in the opposing regimes $l^2\\delta S {{\\ll}} 1$ and $l^2\\delta S{\\gg}1$, we recover the known Onsager-Lifshitz-Roth rules for nondegenerate and exactly-degenerate orbits, respectively. In the absence of crystalline point-group symmetries, three tunable real parameters are needed to attain a spin-degeneracy between two Landau levels; we have exhaustively identified all symmetry classes of orbits for which this number is reduced from three. In particular, only one parameter is needed for rotational-symmetric orbits; this parameter may be the magnitude or orientation of the field, or the bias voltage in tunneling spectroscopy. A signature of single-parameter tunability is a smooth crossover between period-doubled and -undoubled quantum oscillations in the low-temperature, Schubnikov-de Haas effect. We demonstrate the utility of our quantization rule, as well as the tunability of Landau-level degeneracies, for the Rashba two-dimensional electron gas -- subject to an arbitrarily oriented magnetic field, and possibly augmented by the Dresselhaus spin-orbit interaction.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2018-10-03T18:38:43.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "landau quantization",
      "degenerate bands",
      "landau levels",
      "crystalline point-group symmetry",
      "magnetic field"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 23,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}