Magneto-optical properties of gapped-graphene

We theoretically study the optical properties of single-layer graphene placed on hexagonal boron nitride in the presence of a magnetic field. Analytical expressions for the longitudinal χxx(ω) and Hall χyx(ω) susceptibilities are derived from the equation of motion method. The χxx(ω) and χyx(ω) are evaluated as functions of photon energy for both undoped and doped graphenes for different values of electron densities, temperatures, and magnetic fields. The intra-band transitions induce only one peak while the inter-band ones cause a series of peaks that show oscillations with photon energy. The electron density is one of the main factors controlling the threshold energy in the doped regime. The contribution to the susceptibilities of the right polarized light is always dominant in the left polarized one.