Signatures of Bardasis-Schrieffer mode excitation in Third-Harmonic generated currents

We theoretically analyze the collective modes in unconventional superconductors focusing on Bardasis-Schrieffer (BS) mode and its contribution to the third harmonic generation currents. Starting from a model with competing superconducting pairing instabilities we add fluctuations of the fields beyond saddle point approximation and calculate their response to an applied pulsed electric field. To model phase fluctuations appropriately we take into account the effect of the long-range Coulomb interaction. While the phase mode is pushed into a plasmon frequency, as known from the literature, we show that the BS mode remains unaffected. Furthermore, it has a characteristic polarization dependence and, unlike the Higgs mode, generates a current in perpendicular direction to the applied field. We find that the Bardasis-Schrieffer excitations contribute a sizable signal to the third harmonic generated current, which is clearly distinguishable from the charge density fluctuations due to Cooper pair breaking effects and can be straightforwardly detected in experiment.