# Polarization-resolved terahertz third-harmonic generation in a superconductor NbN: dominance of Higgs mode beyond the BCS approximation

## TL;DR

This study demonstrates that in NbN superconductors, the Higgs mode predominantly drives resonant third-harmonic generation in the terahertz range, with polarization-resolved spectroscopy revealing its dominance beyond the BCS approximation.

## Contribution

The paper provides experimental evidence that the Higgs mode dominates THG in NbN, challenging the BCS approximation and highlighting the importance of beyond-BCS effects like retardation.

## Key findings

- Resonant THG appears with polarization parallel to incident light.
- Higgs mode dominates over charge-density fluctuations in NbN.
- Experimental results align with advanced theoretical models beyond BCS.

## Abstract

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.

---
Source: https://tomesphere.com/paper/1703.02815