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 ${\sigma }_{1s}(\omega )$, which origins from the scattering, exhibits a crossover point at $\omega =2|\Delta |$. Particularly, it is further shown that when $\omega <2|\Delta |$, ${\sigma }_{1s}(\omega )$ from the scattering always exhibits a finite value even at low temperature, in contrast to the vanishing ${\sigma }_{1s}(\omega )$ 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 $\pi$-jump at $\omega =|\Delta |$, 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

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Cited by in corpus (7)

• Impurity scattering in superconductors revisited
• A theory of coupled dual dynamics of macroscopic phase coherence and microscopic electronic fluids: effect of dephasing on cuprate superconductivity
• Collisionless dynamics in disordered superconductors
• Diamagnetic property and optical absorption in conventional superconductors with magnetic impurities
• Optical response of Higgs mode in superconductors at clean limit: formulation through Eilenberger equation and Ginzburg-Landau Lagrangian
• Spatially resolved collective modes in d-wave superconductors
• Terahertz nonlinear response in cuprate superconductors and the Higgs field in doped Mott insulators