{
  "abstract": "At a discrete set of ``magic'' twist angles, twisted bilayer graphene develops two bands at charge neutrality that are almost perfectly flat. We present a unified theory of this phenomenon within the chiral continuum model. The central object is the square of the chiral Hamiltonian, a $2\\times2$ Schrödinger operator for an electron moving in a non-Abelian $SU(2)$ pseudo-magnetic field generated by the interlayer tunneling. From it we derive an energy sum rule in which the interlayer coupling splits into a bounded overlap channel and an unbounded current channel; their different scaling with the coupling $α$ explains why the first magic angle is qualitatively different from the rest. The asymptotic rule $α_{m+1}-α_m\\to3/2$ follows from a rescaling of the moiré potential together with its three-cell magnetic periodicity, with the two parity families of zero modes each repeating with period $3$ and interleaved with each other. Near the AA point the zero-mode problem becomes a lowest-Landau-level problem in an effective field $B_{\\rm eff}=3α$, so that the high-order zero modes are coherent Landau states of width $1/\\sqrt{3α}$ whose guiding centres converge to $\\pm(π/3) q_μ$, with kinetic and confinement energies in equipartition. Deforming the coupling into an Abelian one removes the magic-angle sequence, which shows that the non-Abelian structure is essential. Between consecutive magic angles, band inversions at $Γ$ and $M$ produce phases with Chern numbers $C=\\pm2$, and the quantum metric reaches a sharp maximum at $θ\\approx0.43^\\circ$, identifying a promising regime for correlated and topological phases beyond the first magic angle.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.07734",
  "author_total": 2,
  "authors": [
    {
      "name": "Leonardo A. Navarro-Labastida"
    },
    {
      "name": "Gerardo G. Naumis"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/8akm6vad2xfnf.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.07734",
  "fulltext_url": null,
  "id": "8akm6vad2xfnf",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.07734",
  "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"
    ],
    [
      "openalex",
      "2505|Graphene research and applications"
    ]
  ],
  "openalex": "W7220928521",
  "pdf_url": "https://arxiv.org/pdf/2610.07734",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-06",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/8akm6vad2xfnf.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:27:22Z",
      "native_id": "2610.07734",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.07734"
    }
  ],
  "subjects": [
    {
      "field": "physics",
      "origin": "arxiv:cond-mat.mes-hall",
      "subfield": "condensed-matter"
    }
  ],
  "title": "Theory of Magic Angles in Twisted Bilayer Graphene: from Non-Abelian Gauge Fields to Flat Bands",
  "title_text": "Theory of Magic Angles in Twisted Bilayer Graphene: from Non-Abelian Gauge Fields to Flat Bands",
  "type": "preprint",
  "updated_at": "2026-10-30T12:27:22Z",
  "url": "https://research.draconitic.com/paper/8akm6vad2xfnf",
  "venue": "arXiv",
  "versions": []
}