Influence of scattering on optical response of superconductivity

Abstract

By using the gauge-invariant kinetic equation, we analytically investigate the influence of the scattering on the optical properties of superconductors in the normal-skin-effect region. Both linear and second-order responses are studied under a multi-cycle terahertz pulse. In the linear regime, we reveal that the optical absorption $\ddot{I}{ƒ}_{1s}(\ddot{I}‰)$, which origins from the scattering, exhibits a crossover point at $\ddot{I}‰=2|\hat{I}”|$. Particularly, it is further shown that when $\ddot{I}‰<2|\hat{I}”|$, $\ddot{I}{ƒ}_{1s}(\ddot{I}‰)$ from the scattering always exhibits a finite value even at low temperature, in contrast to the vanishing $\ddot{I}{ƒ}_{1s}(\ddot{I}‰)$ in the anomalous-skin-effect region as the Mattis-Bardeen theory revealed. In the second-order regime, responses of the Higgs mode during and after the optical pulse are studied. During the pulse, we show that the scattering causes a phase shift in the second-order response of the Higgs mode. Particularly, this phase shift exhibits a significant $\ddot{I}€$-jump at $\ddot{I}‰=|\hat{I}”|$, which provides a very clear feature for the experimental detection. After the pulse, by studying the damping of the Higgs-mode excitation, we reveal a relaxation mechanism from the elastic scattering, which shows a monotonic enhancement with the increase of the impurity density.

17 pages, 5 figures