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 the introduction of a supercurrent. In a $p+ip$ chiral ground state, these modes can produce peaks in the longitudinal and transverse optical conductivity. Other collective modes belonging to the chiral $p+ip$ order parameter are unaffected by the spin-orbit coupling but contribute to the optical response when a supercurrent is introduced. These results promise avenues for the observation of collective modes in a variety of superconducting systems, including multiband superconductors and superconductors that feature multiple pairing channels or multicomponent order parameters, such as chiral $p$- or $d$-wave superconductors.