  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.
