Spectral theory of twisted bilayer graphene in a magnetic field

TL;DR

This paper investigates the spectral properties of the Bistritzer-MacDonald model of twisted bilayer graphene under magnetic fields, revealing how magnetic fields can distinguish flat band multiplicities via Chern numbers.

Contribution

It demonstrates that magnetic fields can differentiate flat bands of varying multiplicities in twisted bilayer graphene, a novel approach not seen in zero-field conditions.

Findings

Magnetic fields distinguish flat band multiplicities via Chern numbers.

Different interlayer tunneling potentials analyzed, including chiral and anti-chiral limits.

Magnetic field effects provide new insights into the topological properties of the model.

Abstract

In this article we study the Bistritzer-MacDonald (BM) model with external magnetic field. We study the spectral properties of the Hamiltonian in an external magnetic field with a particular emphasis on the flat band of the chiral model at magic angles. Our analysis includes different types of interlayer tunneling potentials, the so-called chiral and anti-chiral limits. One novelty of our article is that we show that using a magnetic field one can discriminate between flat bands of different multiplicities, as they lead to different Chern numbers in the presence of magnetic fields, while for zero magnetic field their Chern numbers always coincide.