Band-selective third-harmonic generation in superconducting MgB2 : Possible evidence for the Higgs amplitude mode in the dirty limit

Abstract

We report on time-resolved linear and nonlinear terahertz spectroscopy of the two-band superconductor $\mathrm{Mg}{\mathrm{B}}_{2}$ with a superconducting transition temperature ${T}_{c}\ensuremath{\approx}36$ K. Third-harmonic generation (THG) is observed below ${T}_{c}$ by driving the system with intense narrow-band THz pulses. For the pump-pulse frequencies $f=0.3$, 0.4, and 0.5 THz, the temperature-dependent evolution of the THG signals exhibits a resonance maximum at the temperatures with the resonance conditions $2f=2{\mathrm{\ensuremath{\Delta}}}_{\ensuremath{\pi}}(T)$ fulfilled, for the dirty-limit superconducting gap $2{\mathrm{\ensuremath{\Delta}}}_{\ensuremath{\pi}}$. In contrast, for $f=0.6$ and 0.7 THz with $2f>2{\mathrm{\ensuremath{\Delta}}}_{\ensuremath{\pi}}(T\ensuremath{\rightarrow}0)=1.03$ THz, the THG intensity increases monotonically with decreasing temperature. Moreover, for $2f<2{\mathrm{\ensuremath{\Delta}}}_{\ensuremath{\pi}}(T\ensuremath{\rightarrow}0)$ the THG is found nearly isotropic with respect to the pump-pulse polarization. These results suggest a predominant contribution of the driven Higgs amplitude mode of the dirty-limit $\ensuremath{\pi}$-band superconducting gap, pointing to the importance of scattering for observation of the Higgs mode in superconductors.