E. V. Gorbar, V. P. Gusynin, A. B. Kuzmenko, S. G. Sharapov
We study the influence of different kinds of gaps in a quasiparticle spectrum on longitudinal and transverse optical conductivities of bilayer graphene. An exact analytical expression for magneto-optical conductivity are derived using a low-energy two-band Hamiltonian. We consider how the layer asymmetry gap caused by a bias electric field and a time-reversal symmetry breaking gap affect the absorption lines. The limit of zero magnetic field is then analyzed for an arbitrary carrier density in the two-band model. For a neutral bilayer graphene the optical Hall and longitudinal conductivities are calculated exactly in the four-band model with four different gaps and zero magnetic field. It is shown that two different time-reversal symmetry breaking states can be distinguished by analyzing the dependence of the optical Hall conductivity on the energy of photon. These time-reversal symmetry breaking states are expected to be observed experimentally via optical polarization rotation either in the Faraday or Kerr effects. We analyze a possibility of a such experiment for a free standing graphene, graphene on a thick substrate and graphene on a double-layer substrate.
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http://arxiv.org/abs/1205.2361
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