{
  "abstract": "We show that the local gauge-invariance of the quantum geometric tensor (QGT) defined in the two-dimensional Block-momentum (BM) space of a generic $N$-band (arising out of sub-lattice degrees of freedom) insulator represented by a tight-binding hamiltonian, leads to the existence of zero modes of non-abelian Dirac operator in such BM space. These zero modes in the two-dimensional Brillouin zone torus $T^{2}$, determines the probability amplitudes associated with the $N$-component ground state wave-function under adiabatic approximation. We analytically derive the expansion coefficients of maximally localized Wannier function in one-dimension from the solutions of these zero mode equations, and obtain momentum-space generalization of celebrated Laughlin gauge condition as a by-product.The commutator of these non-abelian Dirac operators define the algebra of the guiding center co-ordinates which provide a more general frame-work to study such systems than one based on the Landau-level analogues. In the ideal quantum geometric limit, these zero-mode solutions become self-dual momentum-space instantons, and can be linked to the non-abelian generalization of the vortexability criterion of Chern bands in momentum-space. We derive some exact solutions of such zero-mode on the complex torus geometry, and discuss implications of this framework for realistic systems such as two-dimensional topological insulators, rhombohedral $N_{L}$-layer graphene.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2605.27608",
  "author_total": 2,
  "authors": [
    {
      "name": "Neha Kumari"
    },
    {
      "name": "Sankalpa Ghosh"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/28yf2cky8w44s.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2605.27608",
  "fulltext_url": null,
  "id": "28yf2cky8w44s",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2605.27608",
  "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",
      "cond-mat.str-el"
    ],
    [
      "arxiv",
      "hep-th"
    ],
    [
      "openalex",
      "3107|Topological Materials and Phenomena"
    ]
  ],
  "openalex": "W7162672170",
  "pdf_url": "https://arxiv.org/pdf/2605.27608",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-29",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/28yf2cky8w44s.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:25:31Z",
      "native_id": "2605.27608",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2605.27608"
    }
  ],
  "subjects": [
    {
      "field": "physics",
      "origin": "arxiv:cond-mat.mes-hall",
      "subfield": "condensed-matter"
    },
    {
      "field": "physics",
      "origin": "arxiv:hep-th",
      "subfield": "high-energy"
    }
  ],
  "title": "Zero modes of non-abelian Dirac operator in topologically non-trivial band insulator",
  "title_text": "Zero modes of non-abelian Dirac operator in topologically non-trivial band insulator",
  "type": "preprint",
  "updated_at": "2026-10-30T12:25:31Z",
  "url": "https://research.draconitic.com/paper/28yf2cky8w44s",
  "venue": "arXiv",
  "versions": []
}