Interband Theory of Kerr Rotation in Unconventional Superconductors

Abstract

Recent experiments have shown rotation of the plane of polarization of light reflected from the surface of some superconductors. This indicates that time reversal and certain mirror symmetries are broken in the ordered phase. The photon energy exceeds the electronic bandwidth, so that completely filled or completely empty bands must play a role. We show that in strong-coupling theory a Coulomb interaction may produce an order parameter in the unoccupied band that explains the observations. The theory puts tight constraints on the form of the order parameter in different bands. We propose that the experiments have detected, for the first time, the existence of a superconducting order parameter in a band far from the Fermi energy.