Magnetic Response Properties of Twisted Bilayer Graphene

In this article, we analyze the Bistritzer-MacDonald model (also known as the continuum model) of twisted bilayer graphene with an additional external magnetic field. We provide an explicit semiclassical asymptotic expansion of the density of states (DOS) in the limit of strong magnetic fields. We find that unlike for magnetic Schr & ouml;dinger operators, perturbation of the chiral potentials do not expand the Landau bands while perturbations by the anti-chiral potentials do. The explicit expansion of the DOS also enables us to study magnetic response properties such as magnetic oscillations which includes Shubnikov-de Haas and de Haas-van Alphen oscillations as well as the integer quantum Hall effect.