{
  "id": "2409.07383",
  "version": "v1",
  "published": "2024-09-11T16:16:29.000Z",
  "updated": "2024-09-11T16:16:29.000Z",
  "title": "Hofstadter Butterflies in Topological Insulators",
  "authors": [
    "Larry Li",
    "Marcin Abram",
    "Abhinav Prem",
    "Stephan Haas"
  ],
  "comment": "Book chapter. 16 pages, 13 figures",
  "doi": "10.5772/intechopen.1006115",
  "categories": [
    "cond-mat.mes-hall"
  ],
  "abstract": "In this chapter, we investigate the energy spectra as well as the bulk and surface states in a two-dimensional system composed of a coupled stack of one-dimensional dimerized chains in the presence of an external magnetic field. Specifically, we analyze the Hofstadter butterfly patterns that emerge in a 2D stack of coupled 1D Su-Schrieffer-Heeger (SSH) chains subject to an external transverse magnetic field. Depending on the parameter regime, we find that the energy spectra of this hybrid topological system can exhibit topologically non-trivial bulk bands separated by energy gaps. Upon introducing boundaries into the system, we observe topologically protected in-gap surface states, which are protected either by a non-trivial Chern number or by inversion symmetry. We examine the resilience of these surface states against perturbations, confirming their expected stability against local symmetry-preserving perturbations.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2024-09-11T16:16:29.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "hofstadter butterflies",
      "topological insulators",
      "energy spectra",
      "external transverse magnetic field",
      "topologically protected in-gap surface states"
    ],
    "tags": [
      "book chapter",
      "journal article"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 16,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}