Band-selective third-harmonic generation in superconducting MgB$_2$: Possible evidence for Higgs amplitude mode in the dirty limit

TL;DR

This study uses terahertz spectroscopy to observe third-harmonic generation in MgB$_2$, providing evidence for the Higgs amplitude mode in the dirty limit and highlighting the role of scattering in its detection.

Contribution

First observation of Higgs mode contribution to third-harmonic generation in MgB$_2$, emphasizing the impact of scattering in the dirty-limit superconductor.

Findings

Resonance in THG at specific frequencies related to the superconducting gap.

Monotonically increasing THG intensity for frequencies above the gap.

Nearly isotropic THG response for frequencies below the gap.

Abstract

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 temperatures with the resonance conditions $2f=2\Delta_\pi(T)$ fulfilled, for the dirty-limit superconducting gap $2\Delta_\pi$. In contrast, for $f=$ 0.6 and 0.7 THz with $2f>2\Delta_\pi(T\rightarrow0)=1.03$ THz, the THG intensity increases monotonically with decreasing temperature. Moreover, for $2f<2\Delta_\pi(T\rightarrow0)$ 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 $\pi$-band superconducting gap, pointing to the importance of scattering for observation of the Higgs mode in superconductors.