Quasiclassical Theory on Third-Harmonic Generation in Conventional Superconductors with Paramagnetic Impurities

TL;DR

This paper studies how paramagnetic impurities affect third-harmonic generation in superconductors, revealing that impurities suppress the amplitude mode and alter the temperature-dependent THG response, aligning well with experimental observations.

Contribution

It introduces a quasiclassical Green function approach to analyze the impact of paramagnetic impurities on THG in superconductors, highlighting the role of the amplitude mode and symmetry breaking.

Findings

Weak impurities allow a THG peak at the superconducting gap temperature.

Strong impurities suppress the THG peak, indicating amplitude mode disappearance.

Theoretical results agree with experimental data and show negligible diamagnetic effects.

Abstract

We investigate the third-harmonic generation (THG) of s-wave superconductors under microwave pulse irradiation. We consider the effect of paramagnetic impurities on the THG intensity of dirty superconductors. The nonlinear response function is calculated using the method of the quasiclassical Green function. It is shown that the amplitude mode is included as the vertex correction and makes a predominant contribution to the THG intensity. When the effect of paramagnetic impurities is weak, the THG intensity shows a peak at the temperature at which the superconducting gap is about the same as the frequency of the incident pulse, similarly to in experiments. As the effect of paramagnetic impurities is strengthened, the peak of the THG intensity disappears. This indicates that time-reversal symmetry breaking due to paramagnetic impurities eliminates the well-defined amplitude mode. The result of our calculation shows that the existence of the amplitude mode can be confirmed through the THG intensity. The result of a semiquantitative calculation is in good agreement with the experimental result, and it also shows that the diamagnetic term is negligible.