{
  "abstract": "The one-dimensional chain with alternating masses is the simplest mechanical system with a topological band structure. We give a fully analytical account of its localized vibrations built on the complex band structure. The evanescent Bloch waves available at each frequency are matched directly to force balance at a free end or a domain wall, without transfer matrices, which yields closed-form frequencies and decay lengths for every localized mode. The free-end mode sits at a branch point of the complex band structure, where the acoustic and optical sheets join and the decay is fastest. For uniform springs, a sharp wall between the two mass orderings hosts one in-gap mode, symmetric at the light$\\mid$light wall and antisymmetric at the heavy$\\mid$heavy wall, and an adiabatic construction shows that these are the same topological mode; the light$\\mid$light wall also binds a non-topological mode above the optical branch. Spectral unfolding makes this classification visible in momentum space: the sign of the Bloch factor sets the zone-center or zone-boundary character of each mode, and its magnitude sets the width. The Zak phase, quantized by inversion, identifies the modes of topological origin and fixes a half-integer mode count per band at a wall, while the chiral symmetry known to be hidden in strain coordinates explains which frequencies are pinned.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.23300",
  "author_total": 1,
  "authors": [
    {
      "name": "Vincent Meunier"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/8sba8b104medc.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.23300",
  "fulltext_url": null,
  "id": "8sba8b104medc",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.23300",
  "language": null,
  "licence": "CC-BY-NC-ND-4.0",
  "licence_label": "CC BY-NC-ND 4.0",
  "licence_source": "article",
  "licence_url": "http://creativecommons.org/licenses/by-nc-nd/4.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "cond-mat.mes-hall"
    ],
    [
      "openalex",
      "3107|Topological Materials and Phenomena"
    ]
  ],
  "openalex": "W7222953190",
  "pdf_url": "https://arxiv.org/pdf/2610.23300",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-16",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/8sba8b104medc.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:30:32Z",
      "native_id": "2610.23300",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.23300"
    }
  ],
  "subjects": [
    {
      "field": "physics",
      "origin": "arxiv:cond-mat.mes-hall",
      "subfield": "condensed-matter"
    }
  ],
  "title": "Topological edge and domain-wall phonons in the mass-dimerized diatomic chain: complex band structure, Zak phase, and spectral unfolding",
  "title_text": "Topological edge and domain-wall phonons in the mass-dimerized diatomic chain: complex band structure, Zak phase, and spectral unfolding",
  "type": "preprint",
  "updated_at": "2026-10-30T12:33:28Z",
  "url": "https://research.draconitic.com/paper/8sba8b104medc",
  "venue": "arXiv",
  "versions": []
}