  The magneto-optical response of monolayer transition metal dichalcogenides
(TMDs), including excitonic effects, is studied using a nanoribbon geometry. We
compute the diagonal optical conductivity and the Hall conductivity. Comparing
the excitonic optical Hall conductivity to results obtained in the independent
particle approximation, we find an increase in the amplitude corresponding to
one order of magnitude when excitonic effects are included. The Hall
conductivities are used to calculate Faraday rotation spectra for MoS2 and
WSe2. Finally, we have also calculated the diamagnetic shift of the exciton
states of WSe2 in different dielectric environments. Comparing the calculated
diamagnetic shift to recent experimental measurements, we find a very good
agreement between the two.
