Magic angles in twisted bilayer graphene near commensuration: Towards a hypermagic regime

Michael G. Scheer, Kaiyuan Gu, Biao Lian

Research output: Contribution to journalArticlepeer-review

12 Scopus citations


The Bistritzer-MacDonald continuum model (BM model) describes the low-energy moiré bands for twisted bilayer graphene (TBG) at small twist angles. We derive a generalized continuum model for TBG near any commensurate twist angle, which is characterized by complex interlayer hoppings at commensurate AA stackings (rather than the real hoppings in the BM model), a real interlayer hopping at commensurate AB/BA stackings, and a global energy shift. The complex phases of the AA stacking hoppings and the twist angle together define a single angle parameter φ0. We compute the model parameters for the first six distinct commensurate TBG configurations, among which the 38.2° configuration may be within experimentally observable energy scales. We identify the first magic angle for any φ0 at a condition similar to that of the BM model. At this angle, the lowest two moiré bands at charge neutrality become flat except near the ΓM point and retain fragile topology but lose particle-hole symmetry. We further identify a hypermagic parameter regime centered at φ0=±π/2 where many moiré bands around charge neutrality (often 8 or more) become flat simultaneously. Many of these flat bands resemble those in the kagome lattice and px, py 2-orbital honeycomb lattice tight-binding models.

Original languageEnglish (US)
Article number115418
JournalPhysical Review B
Issue number11
StatePublished - Sep 15 2022

All Science Journal Classification (ASJC) codes

  • Electronic, Optical and Magnetic Materials
  • Condensed Matter Physics


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