{
  "abstract": "Most proposals for $Z_3$ parafermions in fractional quantum Hall-superconductor structures used the spin-unpolarized $ν= 2/3$ Halperin $(1,1,2)$ state. The fractional quantum anomalous Hall (FQAH) states of twisted MoTe$_2$ and rhombohedral graphene are believed to be spin- and valley-polarized Jain states, with the same topological order but a different spin structure. We analyze a trench between two polarized $ν= 2/3$ edges. Among the pairing and tunneling bilinears of the edge-mode electrons, exactly two of each have zero conformal spin. Pairing is compatible only with the neutral-mode superconductivity channel and tunneling only with neutral-mode backscattering, whereas in the unpolarized state singlet pairing and tunneling select the same channel. Since the two channels condense the same neutral anyon up to a local operator, the domain walls carry $Z_3$ parafermions, with 3 protected states per pair, whether or not the neutral channel changes between regions; fixing the fermion parity does not enlarge this count. Before the neutral gap forms, pairing is at best marginal for repulsive inter-edge coupling unless an attractive neutral coupling favors its channel; once the gap has formed, both charge terms are relevant for an inter-edge Coulomb coupling below 7/25 of the intra-edge one. The superconductor must supply even-frequency, equal-spin, intravalley pairing, which an s-wave singlet superconductor with only Ising spin-orbit coupling does not provide at leading order, whereas chiral $p+ip$ and $f+if$ states do. The $Z_3$ label is carried by a quasiparticle of the FQAH state, so no process confined to a junction whose tunneling segments are not FQAH can change it, and we expect a $6π$-periodic Josephson current with or without fixed fermion parity.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.01486",
  "author_total": 1,
  "authors": [
    {
      "name": "Aaron Amire"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/8vzap8ca6ggv0.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.01486",
  "fulltext_url": null,
  "id": "8vzap8ca6ggv0",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.01486",
  "language": null,
  "licence": "LicenseRef-arXiv-nonexclusive-1.0",
  "licence_label": "arXiv licence",
  "licence_source": "article",
  "licence_url": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "cond-mat.mes-hall"
    ]
  ],
  "openalex": null,
  "pdf_url": "https://arxiv.org/pdf/2610.01486",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-01",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/8vzap8ca6ggv0.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:26:03Z",
      "native_id": "2610.01486",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.01486"
    }
  ],
  "subjects": [
    {
      "field": "physics",
      "origin": "arxiv:cond-mat.mes-hall",
      "subfield": "condensed-matter"
    }
  ],
  "title": "Parafermions in fractional Chern insulator-superconductor heterostructures: the role of spin polarization",
  "title_text": "Parafermions in fractional Chern insulator-superconductor heterostructures: the role of spin polarization",
  "type": "preprint",
  "updated_at": "2026-10-30T12:26:03Z",
  "url": "https://research.draconitic.com/paper/8vzap8ca6ggv0",
  "venue": "arXiv",
  "versions": []
}