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

TL;DR

This paper generalizes the continuum model for twisted bilayer graphene near any commensurate angle, identifying new magic and hypermagic regimes with flat bands and complex interlayer hoppings, expanding understanding of moiré band phenomena.

Contribution

It introduces a generalized continuum model incorporating complex interlayer hoppings at commensurate angles, revealing new flat band regimes and a hypermagic condition in twisted bilayer graphene.

Findings

First magic angle identified for any phase parameter .

Discovery of a hypermagic regime with many flat bands at  = .

Flat bands exhibit kagome and honeycomb lattice characteristics.

Abstract

The Bistritzer-MacDonald continuum model (BM model) describes the low-energy moir\'e 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 $\phi_0$. We compute the model parameters for the first six distinct commensurate TBG configurations, among which the $38.2^\circ$ configuration may be within experimentally observable energy scales. We identify the first magic angle for any $\phi_0$ at a condition similar to that of the BM model. At this angle, the lowest two moir\'e bands at charge neutrality become flat except near the $\boldsymbol\Gamma_M$ point and retain fragile topology but lose particle-hole symmetry. We further identify a hypermagic parameter regime centered at $\phi_0 = \pm\pi/2$ where many moir\'e bands around charge neutrality (often $8$ or more) become flat simultaneously. Many of these flat bands resemble those in the kagome lattice and $p_x$, $p_y$ 2-orbital honeycomb lattice tight-binding models.