{
  "abstract": "In this work, we revisit the classic Yu-Shiba-Rusinov (YSR) problem of magnetic impurities in $s$-wave superconductors and uncover a quantum geometric origin of the YSR bound-state structure. The key geometric quantity is the momentum-space average of Bloch band projector over low-energy electrons, whose matrix rank, positive eigenvalues, and corresponding eigenvectors directly control the number, energies, and symmetry representations of the YSR states, respectively. As a result, a superconductor with nontrivial normal-state quantum geometry can host more bound states than its trivial counterpart, even if they share the same electronic dispersion. We apply our theory to monolayer $1H$-NbSe$_2$ and find that the geometric texture of its single superconducting band enforces three symmetry-distinct YSR channels for a magnetic point impurity at Nb or Se sites. Our work opens a route to probing normal-state wavefunction geometry through local YSR spectroscopy.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.31920",
  "author_total": 1,
  "authors": [
    {
      "name": "Rui-Xing Zhang"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/2rq4b3by2k7b2.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.31920",
  "fulltext_url": null,
  "id": "2rq4b3by2k7b2",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.31920",
  "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"
    ],
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      "arxiv",
      "cond-mat.str-el"
    ],
    [
      "arxiv",
      "cond-mat.supr-con"
    ],
    [
      "openalex",
      "3104|Physics of Superconductivity and Magnetism"
    ]
  ],
  "openalex": "W7214804624",
  "pdf_url": "https://arxiv.org/pdf/2609.31920",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-25",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/2rq4b3by2k7b2.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:25:12Z",
      "native_id": "2609.31920",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.31920"
    }
  ],
  "subjects": [
    {
      "field": "physics",
      "origin": "arxiv:cond-mat.mes-hall",
      "subfield": "condensed-matter"
    }
  ],
  "title": "Quantum Geometric Origin of Yu-Shiba-Rusinov States",
  "title_text": "Quantum Geometric Origin of Yu-Shiba-Rusinov States",
  "type": "preprint",
  "updated_at": "2026-10-30T12:25:12Z",
  "url": "https://research.draconitic.com/paper/2rq4b3by2k7b2",
  "venue": "arXiv",
  "versions": []
}