  We study the magneto-optical conductivity of a number of Van der Waals
heterostructures, namely, twisted bilayer graphene, AB-AB and AB-BA stacked
twisted double bilayer graphene and monolayer graphene and AB-stacked bilayer
graphene on hexagonal boron nitride. As magnetic field increases, the
absorption spectrum exhibits a self-similar recursive pattern reflecting the
fractal nature of the energy spectrum. Whilst twisted bilayer graphene displays
only weak circular dichroism, monolayer graphene and AB-stacked bilayer
graphene on hexagonal boron nitride show specifically strong circular
dichroism, owing to strong inversion symmetry breaking properties of the
hexagonal boron nitride layer. As, the left and right circularly polarized
light interact with these structures differently, plane polarized incident
light undergoes a Faraday rotation and gains an ellipticity when transmitted.
The size of the respective angles is on the order of a degree.
