Coherent Magneto-Optical Effects in Topological Insulators: Excitation Near the Absorption Edge

We study coherent optics in topological insulator surface states with broken time-reversal symmetry and develop a theory for the dynamical Hall effect driven by intense electromagnetic field. The influence of optical Stark effect enters as nonlinear dependence on the optical field in the resulting Faraday $\theta_F$ and Kerr $\theta_K$ rotations. This nonlinear correction is found to decrease $\theta_F$ with the strength of the A.C. electric field, whereas $\theta_K$ exhibits a non-monotonic behavior. We also assess the effects of relaxation and dephasing on the Hall and magneto-optical responses when the frequency detuning is comparable to the inverse lifetime of the conduction electrons.