From the chiral model of TBG to the Bistritzer--MacDonald model

TL;DR

This paper investigates how the flat bands in the chiral model of twisted bilayer graphene split when including the full Bistritzer--MacDonald model's couplings, revealing symmetry-driven behaviors and the importance of quadratic terms.

Contribution

It provides a detailed analysis of the band splitting mechanism in TBG, connecting the chiral model to the full Bistritzer--MacDonald model and highlighting the role of symmetries and quadratic effects.

Findings

First-order perturbation vanishes at K points due to symmetry.

Band splitting is primarily governed by quadratic terms.

Symmetry considerations explain the flat band behavior.

Abstract

We analyse the splitting of exact flat bands in the chiral model of the twisted bilayer graphene (TBG) when the $AA'/BB'$ coupling of the full Bistritzer--MacDonald model is taken into account. The first-order perturbation caused by the $AA'/BB'$ potential the same for both bands and satisfies interesting symmetries, in particular it vanishes on the line defined by the $K$ points. The splitting of the flat bands is governed by the quadratic term which vanishes at the $K$ points.