{
  "abstract": "We study Dirac points for a two-dimensional scalar Helmholtz equation in a periodic dielectric medium with two penetrable inclusions per honeycomb cell. In a joint small-inclusion and high-contrast regime, we reduce the Bloch eigenvalue problem to a two-dimensional interaction matrix and derive a two-term asymptotic expansion for the two relevant eigenvalues, uniformly for quasi-momenta separated from the reciprocal lattice. At a vertex K of the Brillouin zone, rotation and inversion-conjugation symmetries force these eigenvalues to coincide. A Schur-complement analysis of the exact operator pencil, together with a nonvanishing lattice Green-function coefficient, proves that the resulting double eigenvalue has a nonzero conical splitting and gives an asymptotic formula for the conical slope in the scaled eigenvalue. For fixed sufficiently large contrast, symmetry-preserving changes of variables and analytic perturbation theory then continue this Dirac point as the inclusion size varies: it remains nondegenerate except at a relatively closed discrete set of admissible sizes.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.19426",
  "author_total": 3,
  "authors": [
    {
      "name": "Yi Huang"
    },
    {
      "name": "Bowen Li"
    },
    {
      "name": "Ping Liu"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/bkvm9f5svk2j2.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.19426",
  "fulltext_url": null,
  "id": "bkvm9f5svk2j2",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.19426",
  "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",
      "math.AP"
    ],
    [
      "openalex",
      "2610|Spectral Theory in Mathematical Physics"
    ]
  ],
  "openalex": "W7222136487",
  "pdf_url": "https://arxiv.org/pdf/2610.19426",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-14",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/bkvm9f5svk2j2.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:29:35Z",
      "native_id": "2610.19426",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.19426"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.AP",
      "subfield": "analysis-pdes"
    }
  ],
  "title": "Dirac Points in High-Contrast Dielectric Honeycomb Structures",
  "title_text": "Dirac Points in High-Contrast Dielectric Honeycomb Structures",
  "type": "preprint",
  "updated_at": "2026-10-30T12:29:35Z",
  "url": "https://research.draconitic.com/paper/bkvm9f5svk2j2",
  "venue": "arXiv",
  "versions": []
}