  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.
