Faithful Tight-binding Models and Fragile Topology of Magic-angle Bilayer Graphene

TL;DR

This paper introduces new tight-binding models for magic-angle bilayer graphene that accurately capture flat bands, preserve symmetries, and reveal the fragile topology of these bands, aiding the study of interaction effects.

Contribution

The authors develop a family of symmetric, faithful tight-binding models with 5, 6, or 10 bands per valley and spin, demonstrating the fragile topology of flat bands in twisted bilayer graphene.

Findings

Constructed tight-binding models with preserved symmetries.

Showed the fragile topology of nearly flat bands.

Models serve as optimal starting points for studying interactions.

Abstract

Correlated insulators and superconductivity have been observed in "magic-angle" twisted bilayer graphene, when the nearly flat bands close to neutrality are partially filled. While a momentum-space continuum model accurately describes these flat bands, interaction effects are more conveniently incorporated in tight-binding models. We have previously shown that no fully symmetric tight-binding model can be minimal, in the sense of capturing just the flat bands, so extended models are unavoidable. Here, we introduce a family of tight-binding models that capture the flat bands while simultaneously retaining all symmetries. In particular, we construct three concrete models with five, six, or ten bands per valley and per spin. These models are also faithful, in that the additional degrees of freedom represent energy bands further away from neutrality, and they serve as optimal starting points for a controlled study of interaction effects. Furthermore, our construction demonstrates the "fragile topology" of the nearly flat bands; i.e., the obstruction to constructing exponentially localized Wannier functions can be resolved when a particular set of trivial bands is added to the model.