  Recent advances in time-domain terahertz (THz) spectroscopy have unveiled
that resonantly-enhanced strong THz third-harmonic generation (THG) mediated by
the collective Higgs amplitude mode occurs in s-wave superconductors, where
charge-density fluctuations (CDF) have also been shown to contribute to the
nonlinear third-order susceptibility. It has been theoretically proposed that
the nonlinear responses of Higgs and CDF exhibit essentially different
polarization dependences. Here we experimentally discriminate the two
contributions by polarization-resolved intense THz transmission spectroscopy
for a single-crystal NbN film. The result shows that the resonant THG in the
transmitted light always appears in the polarization parallel to that of the
incident light with no appreciable crystal axis dependence. When we compare
this with the theoretical calculation here with the BCS approximation and the
dynamical mean-field theory for a model of NbN constructed from first
principles, the experimental result strongly indicates that the Higgs mode
rather than the CDF dominates the THG resonance in NbN. A possible mechanism
for this is discussed such as the retardation effect in the phonon-mediated
pairing interaction beyond BCS.
