{
  "id": "2407.20759",
  "version": "v1",
  "published": "2024-07-30T12:02:21.000Z",
  "updated": "2024-07-30T12:02:21.000Z",
  "title": "Origin of Robust $\\mathbb{Z}_2$ Topological Phases in Stacked Hermitian Systems: Non-Hermitian Level Repulsion",
  "authors": [
    "Zhiyu Jiang",
    "Masatoshi Sato",
    "Hideaki Obuse"
  ],
  "comment": "11 pages, 11 figures",
  "categories": [
    "cond-mat.mes-hall",
    "cond-mat.stat-mech",
    "cond-mat.supr-con",
    "quant-ph"
  ],
  "abstract": "Quantum spin Hall insulators, which possess a non-trivial $\\mathbb{Z}_2$ topological phase, have attracted great attention for two decades. It is generally believed that when an even number of layers of the quantum spin Hall insulators are stacked, the $\\mathbb{Z}_2$ topological phase becomes unstable due to $\\mathbb{Z}_2$ nature. While several researchers report counterexamples of the instability, there is no systematic understanding. In this work, we show that the $\\mathbb{Z}_2$ topological phase is robust against the stacking if it has an additional chiral symmetry, in terms of the level repulsion in the corresponding non-Hermitian system. We demonstrate this by mapping a one-dimensional class DIII superconductor with $\\mathbb{Z}_2$ topology to the corresponding non-Hermitian system in AII$^\\dagger$ with $\\mathbb{Z}_2$ point-gap topology.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2024-07-30T12:02:21.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "topological phase",
      "non-hermitian level repulsion",
      "stacked hermitian systems",
      "quantum spin hall insulators",
      "corresponding non-hermitian system"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 11,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}