  Magneto-optical transitions between Landau levels can provide precise
spectroscopic information on the electronic structure and excitation spectra of
graphene, enabling probes of substrate and many-body effects. We calculate the
magneto-optical conductivity of large-size graphene flakes using a
tight-binding approach. Our method allows us to directly compare the
magneto-optical response of an isolated graphene flake with one aligned on
hexagonal boron nitride giving rise to a periodic superlattice potential. The
substrate interaction induces band gaps away from the Dirac point. In the
presence of a perpendicular magnetic field Landau-level like structures emerge
from these zero-field band gaps. The energy dependence of these satellite
structures is, however, not easily accessible by conventional probes of the
density of states by varying the back-gate voltage. Here we propose the
magneto-optical probing of the superlattice perturbed spectrum. Our simulation
includes magneto-excitonic effects in first-order perturbation theory. Our
approach yields a quantitative explanation of recently observed Landau-level
dependent renormalizations of the Fermi velocity.
