Spectral theory of twisted bilayer graphene in a magnetic field

In this article we study the Bistritzer-MacDonald (BM) model with externalmagnetic field. We study the spectral properties of the Hamiltonian in anexternal magnetic field with a particular emphasis on the flat band of thechiral model at magic angles. Our analysis includes different types ofinterlayer 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 candiscriminate between flat bands of different multiplicities, as they lead todifferent Chern numbers in the presence of magnetic fields, while for zeromagnetic field their Chern numbers always coincide.