{
  "id": "2404.07633",
  "version": "v1",
  "published": "2024-04-11T10:52:04.000Z",
  "updated": "2024-04-11T10:52:04.000Z",
  "title": "One-dimensional $\\mathbb{Z}_4$ topological superconductor",
  "authors": [
    "Max Tymczyszyn",
    "Edward McCann"
  ],
  "comment": "7 pages, 5 figures, plus supplementary 12 pages",
  "categories": [
    "cond-mat.mes-hall",
    "cond-mat.supr-con"
  ],
  "abstract": "We describe the mean-field model of a one-dimensional topological superconductor with two orbitals per unit cell. Time-reversal symmetry is absent, but a nonsymmorphic symmetry, involving a translation by a fraction of the unit cell, mimics the role of time-reversal symmetry. As a result, the topological superconductor has $\\mathbb{Z}_4$ topological phases, two which support Majorana bound states and two which do not, in agreement with a prediction based on K-theory classification [K. Shiozaki et al., Phys. Rev. B 93, 195413 (2016)]. As with the Kitaev chain, the presence of Majorana bound states gives rise to the $4\\pi$-periodic Josephson effect. The K-theory classification describes two $\\mathbb{Z}_4$ subclasses, but, by identifying models in both subclasses, we show that they are related by a unitary transformation and are equivalent.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2024-04-11T10:52:04.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "time-reversal symmetry",
      "support majorana bound states",
      "unit cell",
      "k-theory classification",
      "periodic josephson effect"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 7,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}