{
  "abstract": "Flat bands amplify interactions into correlated phases, and topological bound states are robust by principle; combining the two in a model that is both exactly analyzable and experimentally accessible is therefore especially desirable. Here we show that a square-lattice model with a slowly modulated Dirac mass texture, $m(x)=m+m_0\\cos(2πx/L)$ with $L$ up to hundreds of sites, provides such a setting, without engineered geometries, lattice-scale textures, or long-range hoppings. Exact nesting reduces the problem, independently at each transverse momentum $k_y$, to a $1+1$ dimensional Dirac Hamiltonian with a position-dependent mass: every simple zero of $m(x)$ binds Jackiw-Rebbi zero modes, and the two walls of a period form an effective Su-Schrieffer-Heeger ring. The model interpolates between a chirally pinned flat band at large $L$, a helical miniband whose nodes are enforced by a boundary phase of the ring, and a bias-dimerized regime in which the sign of the bias sets a winding number. A central result is that the miniband bandwidth is not a single scale: a max-min measurement conflates three widths of different origin, the helical height $W_{\\rm JR}$ exponential in the period, the zone-edge upturn $W_{\\rm edge}\\propto L^{-2/3}$ dominating at large $L$, and a bias bump exponential in $L$, so the flat band is robust against bias in the thermodynamic limit. We analyze two lattice realizations, a two-orbital model with modulated inter-orbital hybridization and a single-orbital bond-order texture sharing the nodal physics while leaving the van Hove points gapless, and propose experiments on cold-atom superlattices, Kekule-ordered graphene, STM designer lattices, and microwave arrays.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.16183",
  "author_total": 1,
  "authors": [
    {
      "name": "Tao Zhou"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/abhv7f4mzbrwr.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.16183",
  "fulltext_url": null,
  "id": "abhv7f4mzbrwr",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.16183",
  "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",
      "cond-mat.mes-hall"
    ],
    [
      "arxiv",
      "cond-mat.mtrl-sci"
    ],
    [
      "arxiv",
      "cond-mat.quant-gas"
    ],
    [
      "openalex",
      "3107|Topological Materials and Phenomena"
    ]
  ],
  "openalex": "W7221787205",
  "pdf_url": "https://arxiv.org/pdf/2610.16183",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-12",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/abhv7f4mzbrwr.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:29:06Z",
      "native_id": "2610.16183",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.16183"
    }
  ],
  "subjects": [
    {
      "field": "physics",
      "origin": "arxiv:cond-mat.quant-gas",
      "subfield": "amo"
    },
    {
      "field": "physics",
      "origin": "arxiv:cond-mat.mes-hall",
      "subfield": "condensed-matter"
    }
  ],
  "title": "Chirally pinned flat bands, helical minibands, and bias-controlled topology of Jackiw-Rebbi states in a periodically modulated Dirac mass texture",
  "title_text": "Chirally pinned flat bands, helical minibands, and bias-controlled topology of Jackiw-Rebbi states in a periodically modulated Dirac mass texture",
  "type": "preprint",
  "updated_at": "2026-10-30T12:29:06Z",
  "url": "https://research.draconitic.com/paper/abhv7f4mzbrwr",
  "venue": "arXiv",
  "versions": []
}