Integrability in the chiral model of magic angles

TL;DR

This paper investigates the properties of magic angles in the chiral model of twisted bilayer graphene, demonstrating the infinitude of such angles, establishing the existence of the first real magic angle, and suggesting hidden integrability.

Contribution

It introduces a method to sum over powers of magic angles, proves the existence of the first real magic angle, and provides evidence for integrability in the chiral model.

Findings

Set of magic angles is infinite.

Existence of the first real magic angle proven.

Flat band at zero energy has minimal multiplicity.

Abstract

Magic angles in the chiral model of twisted bilayer graphene are parameters for which the chiral version of the Bistritzer--MacDonald Hamiltonian exhibits a flat band at energy zero. We compute the sums over powers of (complex) magic angles and use that to show that the set of magic angles is infinite. We also provide a new proof of the existence of the first real magic angle, showing also that the corresponding flat band has minimal multiplicity for the simplest possible choice of potentials satisfying all symmetries. These results indicate (though do not prove) a hidden integrability of the chiral model.