Quantum magneto-optics of the graphite family

The optical conductivity of graphene, bilayer graphene, and graphite in quantizing magnetic fields is studied. Both dynamical conductivities, longitudinal and Hall's, are evaluated analytically. The conductivity peaks are explained in terms of electron transitions. Correspondences between the transition frequencies and the magneto-optical features are established using the theoretical results. We show that trigonal warping can be considered within the perturbation theory for strong magnetic fields larger than 1 T. The semiclassical approach is applied for weak fields when the Fermi energy is much larger than the cyclotron frequency. The main optical transitions obey the selection rule with Delta n = 1 for the Landau number n, but the Delta n = 2 transitions due to the trigonal warping are also possible. The Faraday/Kerr rotation and light transmission/reflection in quantizing magnetic fields are calculated. Parameters of the Slonczewski-Weiss-McClure model are used in the fit taking the previous de Haas-van Alphen measurements into account and correcting some of them in the case of strong magnetic fields.