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Register a new userBand-Selective Third-Harmonic Generation in Superconducting MgB$_2$: Evidence for Higgs Amplitude Mode in the Dirty Limit
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We report on time-resolved linear and nonlinear terahertz spectroscopy of the two-band superconductor MgB$_2$ with the superconducting transition temperature $T_c approx$ 36 K. Third-harmonic generation (THG) is observed below $T_c$ by driving the system with intense narrowband THz pulses. For the pump-pulse frequencies $f=$ 0.3, 0.4, and 0.5 THz, temperature-dependent evolution of the THG signals exhibits a resonance maximum at the temperature where $2f=2Delta_pi(T)$, for the dirty-limit superconducting gap $2Delta_pi=$ 1.03 THz at 4 K. In contrast, for $f=$ 0.6 and 0.7 THz with $2f>2Delta_pi$, the THG intensity increases monotonically with decreasing temperature. Moreover, for $2f<2Delta_pi$ the THG is found nearly isotropic with respect to the pump-pulse polarization. These results suggest the predominant contribution of the driven Higgs amplitude mode of the dirty-limit gap, pointing to the importance of scattering for observation of the Higgs mode in superconductors.
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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.
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