Influence of scattering on the optical response of superconductors

Abstract

By using the gauge-invariant kinetic equation [Yang and Wu, Phys. Rev. B 98, 094507 (2018); Yang and Wu, Phys. Rev. B 100, 104513 (2019)], 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 multicycle terahertz pulse. In the linear regime, we reveal that the optical absorption σ1s(ω), induced by the scattering, exhibits a crossover point at ω=2|Δ|. Particularly, it is further shown that when ω<2|Δ|, σ1s(ω) from the scattering always exhibits a finite value even at low temperature, in contrast to the vanishing σ1s(ω) in the anomalous-skin-effect region as the Mattis-Bardeen theory [Mattis and Bardeen, Phys. Rev. 111, 412 (1958)] 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 π jump at ω=|Δ|, 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.

Similar papers