Magneto-optical properties of topological insulator thin films with broken inversion symmetry

We determine the optical response of ultrathin film topological insulators in the presence of a quantizing external magnetic field taking into account both hybridization between surface states, broken inversion symmetry and explicit time reversal symmetry breaking by the magnetic field. We find that breaking of inversion symmetry in the system, which can be due to interaction with a substrate or electrical gating, results in Landau level crossings which lead to additional optical transition channels that were previously forbidden. We show that by tuning the hybridization and symmetry breaking parameters, a transition from the normal to a topological insulator phase occurs with measurable signatures in both the longitudinal and optical Hall conductivity.