{
  "abstract": "The equivalence between the axion invariant and the $S_4$ symmetry indicator is established for three-dimensional $S_4$-symmetric axion insulators with vanishing three-dimensional Chern numbers. Starting from the Chern-Simons expression for the magnetoelectric polarizability, $2P_3=θ/π$ is rewritten in terms of the $S_4$ sewing matrix. After stable reduction to determinant-one two-band blocks, the invariant is expressed as the degree of a map from the Brillouin zone to $SU(2)$. The degree modulo two is then evaluated from the $S_4$ eigenvalues at the four $S_4$-invariant momenta and is shown to coincide with the symmetry indicator $z_2$. A minimal tight-binding model with $S_4$ symmetry verifies the correspondence between $2P_3$ and $z_2$ throughout its phase diagram. The result closes a gap between the topological-field-theory description of the axion response and the topological-band-theory classification by symmetry indicators. It also extends the known response-indicator equivalence from antiunitary settings such as $C_nT$ symmetry to the unitary, orientation-reversing roto-inversion symmetry $S_4$.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": "Journal reference: 2026 J. Phys.: Condens. Matter 38 445501",
  "arxiv": "2607.05719",
  "author_total": 1,
  "authors": [
    {
      "name": "Mengyao Zhang"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/1cvbmmcyzkqsz.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2607.05719",
  "fulltext_url": null,
  "id": "1cvbmmcyzkqsz",
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  "landing_url": "https://arxiv.org/abs/2607.05719",
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  "licence_label": "arXiv licence",
  "licence_source": "article",
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  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "cond-mat.mes-hall"
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      "openalex",
      "3107|Topological Materials and Phenomena"
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  "openalex": "W7167710532",
  "pdf_url": "https://arxiv.org/pdf/2607.05719",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-28",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/1cvbmmcyzkqsz.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:25:12Z",
      "native_id": "2607.05719",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2607.05719"
    }
  ],
  "subjects": [
    {
      "field": "physics",
      "origin": "arxiv:cond-mat.mes-hall",
      "subfield": "condensed-matter"
    }
  ],
  "title": "Equivalence between the Axion Invariant and the $S_4$ Symmetry Indicator",
  "title_text": "Equivalence between the Axion Invariant and the S_4 Symmetry Indicator",
  "type": "preprint",
  "updated_at": "2026-11-05T15:20:17Z",
  "url": "https://research.draconitic.com/paper/1cvbmmcyzkqsz",
  "venue": "arXiv",
  "versions": [
    {
      "doi": "10.1088/1361-648x/aeb781",
      "pid": null,
      "relation": "published-as",
      "title": null,
      "venue": null
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}