Optical conductivity of superconductors with supercurrent

In this work we show how the presence of a supercurrent can lead to non-zero optical conductivity in the clean limit, even in single band superconductors. Such interband transitions are forbidden in usual circumstances due to particle-hole and inversion symmetries, therefore requiring strong disorder as described by Mattis and Bardeen. Our approach circumvents this limitation and in conjunction with using the screening supercurrent arising from the external magnetic field enables a detailed investigation of the superconducting state. In particular, we focus on the cases of parabolic bands and Dirac fermions with s-wave order parameter, and parabolic bands with d-wave order parameter. We demonstrate how optical conductivity can be used both to distinguish the nature of the underlying normal state, as well as the type of the superconducting order parameter.