Current-Enabled Optical Conductivity of Collective Modes in Unconventional Superconductors

We theoretically investigate the current-enabled linear optical conductivity of collective modes in superconductors with unconventional pairing symmetries. After deriving general formulas for the optical conductivity of a superconductor featuring multiple pairing channels and bands using the path integral formalism, we apply these formulas to several models. Using a model of competing s- and d-wave pairing interactions, we find that several known collective modes generate peaks in the optical conductivity upon injection of a supercurrent. This includes single- and multiband versions of Bardasis-Schrieffer modes, mixed-symmetry Bardasis-Schrieffer modes, and Leggett modes. Using a model for interband p-wave superconductivity with Rashba spin-orbit coupling, we find that in such a system Bardasis-Schrieffer modes are optically active even without introducing a supercurrent. In a p+ip chiral ground state, these modes turn out to produce peaks in the longitudinal and transverse optical conductivity. Other collective modes belonging to the chiral p+ip order parameter turn out to be unaffected by the spin-orbit coupling but contribute to the optical response when a supercurrent is introduced. These results promise new avenues for the observation of collective modes in a variety of superconducting systems, including multiband superconductors and superconductors that feature multiple pairing channels or multi-component order parameters, such as chiral p- or d-wave superconductors.