{
  "abstract": "Quantized Hall transport is traditionally anchored to a bulk spectral gap, which isolates the occupied subspace and exponentially suppresses thermal deviations. Recently discovered critical topological flat bands (CTFBs) challenge this paradigm: an exactly flat band touches a dispersive continuum while retaining a well-defined integer Chern number. However, their finite-temperature transverse transport properties remain entirely unexplored. Here, we develop a low-temperature theory of the intrinsic electrical, thermoelectric, and thermal Hall responses in CTFBs. At fixed particle number, the macroscopic flat-band degeneracy forces a singular Lambert-$W$ drift of the chemical potential, generating an algebraic-logarithmic hierarchy of low-temperature corrections: $T\\ln(1/T)$ for electrical Hall, $T[\\ln(1/T)]^2$ for thermoelectric Hall, and $T[\\ln(1/T)]^3$ for thermal Hall conductivity, replacing the activated thermal protection of a gapped Chern insulator. By contrast, externally pinning the chemical potential to the flat-band energy locks the flat band to half occupation at any nonzero temperature, obstructing the recovery of the fully filled topological ground state as $T\\to0^+$. Our results establish that a bulk spectral gap is unnecessary for zero-temperature Hall quantization, but indispensable for its exponential thermal protection.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.40065",
  "author_total": 3,
  "authors": [
    {
      "name": "Chang-geun Oh"
    },
    {
      "name": "Tomoki Ozawa"
    },
    {
      "name": "Jun-Won Rhim"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/c30g3c9mkbgzs.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.40065",
  "fulltext_url": null,
  "id": "c30g3c9mkbgzs",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.40065",
  "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"
    ],
    [
      "arxiv",
      "cond-mat.str-el"
    ],
    [
      "openalex",
      "3107|Topological Materials and Phenomena"
    ]
  ],
  "openalex": "W7215073346",
  "pdf_url": "https://arxiv.org/pdf/2609.40065",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-30",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/c30g3c9mkbgzs.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:25:49Z",
      "native_id": "2609.40065",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.40065"
    }
  ],
  "subjects": [
    {
      "field": "physics",
      "origin": "arxiv:cond-mat.mes-hall",
      "subfield": "condensed-matter"
    }
  ],
  "title": "Topological Transverse Transport without a Gap in Critical Topological Flat Bands",
  "title_text": "Topological Transverse Transport without a Gap in Critical Topological Flat Bands",
  "type": "preprint",
  "updated_at": "2026-10-30T12:25:49Z",
  "url": "https://research.draconitic.com/paper/c30g3c9mkbgzs",
  "venue": "arXiv",
  "versions": []
}