{
  "abstract": "In the BCS theory of superconductivity the amplitude (Higgs) mode is degenerate with the pair-breaking threshold: its frequency coincides with $2Δ$, so it is an edge singularity rather than a true collective mode. This is why after a sudden weak perturbation at $t=0$ its oscillations decay algebraically as $1/\\sqrt{t}$. We show that the retardation effects due to the phonon dynamics in the strong-coupling theory lift this degeneracy. The Higgs mode detaches from the pair-breaking edge $2Δ_g$, set by the spectral gap, and becomes a sharp subgap excitation. We determine its frequency from the longitudinal pair susceptibility evaluated directly on the real frequency axis, using the Eilenberger equations for Migdal--Eliashberg theory with the Einstein phonon spectrum. The response of the mass renormalization supplies at least two fifths of the displacement, and possibly all of it: with it switched off, the binding falls below the resolution of the calculation. Its consequences, however, are significant because a percent-level shift transfers about a quarter of the spectral weight of the amplitude channel out of the two-quasiparticle continuum into a discrete energy level. What experiment sees is therefore not the displacement itself but its consequence: amplitude oscillations that persist instead of decaying as $1/\\sqrt{t}$.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.10826",
  "author_total": 2,
  "authors": [
    {
      "name": "Maxim Dzero"
    },
    {
      "name": "Emil A. Yuzbashyan"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/0jc3t75nde1zg.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.10826",
  "fulltext_url": null,
  "id": "0jc3t75nde1zg",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.10826",
  "language": null,
  "licence": "CC-BY-4.0",
  "licence_label": "CC BY 4.0",
  "licence_source": "article",
  "licence_url": "http://creativecommons.org/licenses/by/4.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "cond-mat.str-el"
    ],
    [
      "arxiv",
      "cond-mat.supr-con"
    ],
    [
      "openalex",
      "3104|Physics of Superconductivity and Magnetism"
    ]
  ],
  "openalex": "W7221158931",
  "pdf_url": "https://arxiv.org/pdf/2610.10826",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-15",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/0jc3t75nde1zg.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:30:32Z",
      "native_id": "2610.10826",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.10826"
    }
  ],
  "subjects": [
    {
      "field": "physics",
      "origin": "arxiv:cond-mat.str-el",
      "subfield": "condensed-matter"
    }
  ],
  "title": "Amplitude mode in Eliashberg superconductors",
  "title_text": "Amplitude mode in Eliashberg superconductors",
  "type": "preprint",
  "updated_at": "2026-10-30T12:33:28Z",
  "url": "https://research.draconitic.com/paper/0jc3t75nde1zg",
  "venue": "arXiv",
  "versions": []
}