paper

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

arXiv:2203.06163 · doi:10.1103/PhysRevB.106.115418

Abstract

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 stackings (rather than the real hoppings in the BM model), a real interlayer hopping at commensurate stackings, and a global energy shift. The complex phases of the stacking hoppings and the twist angle together define a single angle parameter . We compute the model parameters for the first six distinct commensurate TBG configurations, among which the configuration may be within experimentally observable energy scales. We identify the first magic angle for any 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 point and retain fragile topology but lose particle-hole symmetry. We further identify a hypermagic parameter regime centered at where many moiré bands around charge neutrality (often or more) become flat simultaneously. Many of these flat bands resemble those in the kagome lattice and , 2-orbital honeycomb lattice tight-binding models.

arXiv comment49 pages, 22 figures, accepted by Physical Review B

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