Band-selective third-harmonic generation in superconducting <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:msub><mml:mi mathvariant="normal">MgB</mml:mi><mml:mn>2</mml:mn></mml:msub></mml:math> : Possible evidence for the Higgs amplitude mode in the dirty limit

We report on time-resolved linear and nonlinear terahertz spectroscopy of the two-band superconductor MgB$_2$ with superconducting transition temperature $T_c \approx 36$ K. Third-harmonic generation (THG) is observed below $T_c$ by driving system intense narrowband THz pulses. For pump-pulse frequencies $f=$ 0.3, 0.4, 0.5 THz, temperature-dependent evolution THG signals exhibits a resonance maximum at temperatures conditions $2f=2\Delta_\pi(T)$ fulfilled, for dirty-limit gap $2\Delta_\pi$. In contrast, 0.6 0.7 $2f>2\Delta_\pi(T\rightarrow0)=1.03$ intensity increases monotonically decreasing temperature. Moreover, $2f<2\Delta_\pi(T\rightarrow0)$ found nearly isotropic respect to polarization. These results suggest predominant contribution driven Higgs amplitude mode $\pi$-band gap, pointing importance scattering observation in superconductors.