{
  "id": "2304.13118",
  "version": "v1",
  "published": "2023-04-25T19:46:09.000Z",
  "updated": "2023-04-25T19:46:09.000Z",
  "title": "Response to polarization and weak topology in Chern insulators",
  "authors": [
    "Sachin Vaidya",
    "Mikael C. Rechtsman",
    "Wladimir A. Benalcazar"
  ],
  "categories": [
    "cond-mat.mes-hall",
    "physics.optics"
  ],
  "abstract": "Chern insulators present a topological obstruction to a smooth gauge in their Bloch wave functions that prevents the construction of exponentially-localized Wannier functions - this makes the electric polarization ill-defined. Here, we show that spatial or temporal differences in polarization within Chern insulators are well-defined and physically meaningful because they account for bound charges and adiabatic currents. We further show that the difference in polarization across Chern-insulator regions can be quantized in the presence of crystalline symmetries, leading to \"weak\" symmetry-protected topological phases. These phases exhibit charge fractional quantization at the edge and corner interfaces and with concomitant topological states. We also generalize our findings to quantum spin-Hall insulators and 3D topological insulators. Our work settles a long-standing question and deems the bulk polarization as the fundamental quantity with a \"bulk-boundary correspondence\", regardless of whether a Wannier representation is possible.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2023-04-25T19:46:09.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "chern insulators",
      "weak topology",
      "bloch wave functions",
      "quantum spin-hall insulators",
      "charge fractional quantization"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}