{
  "abstract": "We study the quantum transport of Dirac electrons in graphene subjected to a polyadic Cantor-structured electrostatic potential. Using the superperiodic potential formalism, we obtain a closed-form expression for the transmission probability. As the Cantor stage increases, the transmission spectrum evolves from a sparse set of superlattice resonances to a near-transparent regime, with the polyadic order setting the rate of this evolution. The angular response depends on the doping configuration, showing distinct behavior in the $n$--$n$--$n$, $n$--$p$--$n$, and Dirac-point cases. In the near-transparent regime, the transmission follows double-logarithmic scaling laws with respect to four independent control parameters: the Cantor stage, the potential height, the initiator length, and the angle of incidence. By combining these individual scaling relations, we establish a unified scaling law governing quantum transport. These results show that the hierarchical self-similarity of the potential governs the transport properties of such systems.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2608.28398",
  "author_total": 3,
  "authors": [
    {
      "name": "Sudhanshu Shekhar"
    },
    {
      "name": "Mohammad Umar"
    },
    {
      "name": "Bhabani Prasad Mandal"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/0xvvbhycmbycj.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2608.28398",
  "fulltext_url": null,
  "id": "0xvvbhycmbycj",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2608.28398",
  "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",
      "cond-mat.mes-hall"
    ],
    [
      "arxiv",
      "hep-th"
    ],
    [
      "arxiv",
      "math-ph"
    ],
    [
      "arxiv",
      "math.MP"
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    [
      "arxiv",
      "quant-ph"
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    [
      "openalex",
      "2505|Graphene research and applications"
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  "openalex": "W7204770696",
  "pdf_url": "https://arxiv.org/pdf/2608.28398",
  "pmcid": null,
  "pmid": null,
  "published": "2026-08-28",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/0xvvbhycmbycj.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:17:22Z",
      "native_id": "2608.28398",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2608.28398"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math-ph",
      "subfield": "mathematical-physics"
    },
    {
      "field": "physics",
      "origin": "arxiv:cond-mat.mes-hall",
      "subfield": "condensed-matter"
    },
    {
      "field": "physics",
      "origin": "arxiv:hep-th",
      "subfield": "high-energy"
    },
    {
      "field": "physics",
      "origin": "arxiv:quant-ph",
      "subfield": "quantum"
    }
  ],
  "title": "Quantum transport and unified scaling law in graphene with polyadic Cantor electrostatic barriers",
  "title_text": "Quantum transport and unified scaling law in graphene with polyadic Cantor electrostatic barriers",
  "type": "preprint",
  "updated_at": "2026-10-30T12:17:28Z",
  "url": "https://research.draconitic.com/paper/0xvvbhycmbycj",
  "venue": "arXiv",
  "versions": []
}