{
  "abstract": "This paper analyzes the quantized asymmetric transport along the boundary of a two-dimensional topological insulator occupying a half plane, or along the interface separating two insulators. In contrast with problems posed on the Euclidean plane, terminating a sample requires a choice of self-adjointrealization, $H_L$, and we show that a quantized transport depends on that choice. The physical observable modeling the asymmetric transport is the edge, or interface, current $σ_I[H_L]=\\Tr\\,i[H_L,P]φ'(H_L)$. It is shown to be well defined along two routes. For Shapiro--Lopatinski elliptic realizations, we use estimates from Boutet de Monvel's calculus to show that the current observable is a well-defined trace, that $\\mathcal I=2πσ_I[H_L]$ is a Fredholm index, and that it is stable under deformations and compactly supported changes of the operator and of its termination. For translation invariant operators along the edge, a spectral analysis defines $\\mathcal I$ when the edge spectrum escapes a bulk gap at large momenta. $\\mathcal I$ is then also a spectral flow and a Maslov index. Our main theorem is a bulk--edge correspondence \\[ \\mathcal I=\\cR-\\cR_L+η\\bigl(L_\\infty,\\Lm^Φ(+)\\bigr)-η\\bigl(L_\\infty,\\Lm^Φ(-)\\bigr), \\] We determine the range of $\\mathcal I$. We extend the formula to interfaces with arbitrary transmission conditions. At the transparent condition, the invariant equals the bulk-difference invariant of the Euclidean plane. Eight examples illustrate the theoretical findings.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.05616",
  "author_total": 1,
  "authors": [
    {
      "name": "Guillaume Bal"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/53dwk4zj886jf.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.05616",
  "fulltext_url": null,
  "id": "53dwk4zj886jf",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.05616",
  "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",
      "math-ph"
    ],
    [
      "arxiv",
      "math.MP"
    ],
    [
      "openalex",
      "3107|Topological Materials and Phenomena"
    ]
  ],
  "openalex": "W7220699448",
  "pdf_url": "https://arxiv.org/pdf/2610.05616",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-04",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/53dwk4zj886jf.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:27:01Z",
      "native_id": "2610.05616",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.05616"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math-ph",
      "subfield": "mathematical-physics"
    }
  ],
  "title": "A bulk--edge correspondence for two-dimensional self-adjoint boundary and interface problems",
  "title_text": "A bulk--edge correspondence for two-dimensional self-adjoint boundary and interface problems",
  "type": "preprint",
  "updated_at": "2026-10-30T12:27:10Z",
  "url": "https://research.draconitic.com/paper/53dwk4zj886jf",
  "venue": "arXiv",
  "versions": []
}