Fine structure of flat bands in a chiral model of magic angles

TL;DR

This paper investigates the symmetry properties and structure of flat bands in a chiral model of twisted bilayer graphene at magic angles, revealing conditions for flat band existence and their nodal set relationships.

Contribution

It provides a symmetry-based analysis of flat bands in the chiral TBG model and links flat band multiplicity to eigenfunction nodal sets.

Findings

Vanishing of the first Bloch eigenvalue at Dirac points implies flat bands.

Flat band multiplicity relates to the nodal set of eigenfunctions.

Numerical observations on the structure of flat bands.

Abstract

We analyze symmetries of Bloch eigenfunctions at magic angles for the Tarnopolsky--Kruchkov--Vishwanath chiral model of the twisted bilayer graphene (TBG) following the framework introduced by Becker--Embree--Wittsten--Zworski. We show that vanishing of the first Bloch eigenvalue away from the Dirac points implies its vanishing at all momenta, that is the existence of a flat band. We also show how the multiplicity of the flat band is related to the nodal set of the Bloch eigenfunctions. We conclude with two numerical observations about the structure of flat bands.