Revealing novel aspects of light-matter coupling in terahertz two-dimensional coherent spectroscopy: the case of the amplitude mode in superconductors

TL;DR

This study uses terahertz two-dimensional coherent spectroscopy to explore the nonlinear response of superconductors, revealing how disorder and collective modes influence the amplitude mode near the superconducting gap.

Contribution

It demonstrates the capability of THz 2DCS to detect amplitude modes and disorder effects in superconductors, providing insights inaccessible to other spectroscopic methods.

Findings

Resonance at twice the superconducting gap energy ($2\Delta$) observed with broad-band THz pulses.

Resonant enhancement at the driving frequency $\Omega$ when $\Omega = 2\Delta$ with narrow-band pulses.

Amplitude mode dominates the $\Omega=2\Delta$ resonance across disorder levels.

Abstract

Recently developed terahertz (THz) two-dimensional coherent spectroscopy (2DCS) is a powerful technique to obtain materials information in a fashion qualitatively different from other spectroscopies. Here, we utilized THz 2DCS to investigate the THz nonlinear response of conventional superconductor NbN. Using broad-band THz pulses as light sources, we observed a third-order nonlinear signal whose spectral components are peaked at twice the superconducting gap energy $2\Delta$. With narrow-band THz pulses, a THz nonlinear signal was identified at the driving frequency $\Omega$ and exhibited a resonant enhancement at temperature when $\Omega = 2\Delta$. General theoretical considerations show that such a resonance can only arise from a disorder-activated paramagnetic coupling between the light and the electronic current. This proves that the nonlinear THz response can access processes distinct from the diamagnetic Raman-like density fluctuations, which are believed to dominate the nonlinear response at optical frequencies in metals. Our numerical simulations reveal that even for a small amount of disorder, the $\Omega=2\Delta$ resonance is dominated by the superconducting amplitude mode over the entire investigated disorder range. This is in contrast to other resonances, whose amplitude-mode contribution depends on disorder. Our findings demonstrate the unique ability of THz 2DCS to explore collective excitations inaccessible in other spectroscopies.