Orbital optical activity in noncentrosymmetric metals and superconductors

We present the optical activity induced by the orbital magnetic moment in metals and superconductors using Green's function formalization. Usually, an apparent singularity of the optical activity vanishes in the normal state; however, we show that it remains finite in the superconducting state and is related to the superconducting Edelstein effect, ensuring the missing area measurement. Finally, we calculate the optical activity in a model Hamiltonian mimicking doped transition metal dichalcogenides to investigate its characteristic spectrum, which reveals a peak shift caused by the interband Fermi surface, its relation with the orbital magnetic moment, and the change of the spectrum in a superconductor at low frequency. We also analyze the optical rotation to discuss the possibility of observing the optical activity in experiments.