{
  "id": "2311.17859",
  "version": "v1",
  "published": "2023-11-29T18:04:56.000Z",
  "updated": "2023-11-29T18:04:56.000Z",
  "title": "$\\mathbb{Z}_{2}=0$ is topological too",
  "authors": [
    "Chao Lei",
    "Perry T. Mahon",
    "Allan H. MacDonald"
  ],
  "comment": "6+13 pages, 4 figures, comments welcome",
  "categories": [
    "cond-mat.mes-hall",
    "cond-mat.quant-gas"
  ],
  "abstract": "The electronic ground state of a three-dimensional (3D) band insulator with time-reversal ($\\Theta$) symmetry or time-reversal times a discrete translation ($\\Theta T_{1/2}$) symmetry is classified by a $\\mathbb{Z}_{2}$-valued topological invariant and characterized by quantized magnetoelectric response. Here we demonstrate by explicit calculation in model $\\mathbb{Z}_{2}$ topological insulator thin-films that whereas the magnetoelectric response is localized at the surface in the $\\Theta$ symmetry (non-magnetic) case, it is non-universally partitioned between surface and interior contributions in the $\\Theta T_{1/2}$ (anti-ferromagnetic) case, while remaining quantized. Within our model the magnetic field induced polarization arises entirely from an anomalous ${\\cal N}=0$ Landau level subspace within which the projected Hamiltonian is a generalized Su-Schrieffer-Heeger model whose topological properties are consistent with those of the starting 3D model.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2023-11-29T18:04:56.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "topological",
      "magnetic field induced polarization arises",
      "electronic ground state",
      "landau level subspace",
      "time-reversal times"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 13,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}