Surface resistance and amplitude mode under uniform and static external field in conventional superconductors

TL;DR

This paper investigates the surface resistance and amplitude mode response of s-wave superconductors under static external fields, comparing dirty and clean cases through numerical calculations within the quasiclassical approximation.

Contribution

It provides a nonperturbative analysis of static field effects on surface resistance and reveals the behavior of the amplitude mode in both dirty and clean superconductors.

Findings

Amplitude mode appears in both dirty and clean cases.

Discrepancy in excitation energy of the amplitude mode in clean superconductors.

Qualitative agreement with experimental results.

Abstract

We calculate the surface resistance of s-wave superconductors under a static external field on the basis of the quasiclassical approximation. The numerical calculations are performed both for the dirty and relatively clean cases, and the difference in the absorption spectrum between them is investigated. The amplitude mode in the dirty case, which has been previously studied in the local response function, appears also in the nonlocal response. In the clean case, there is a large discrepancy between the excitation energy of the amplitude mode and the energy of the gap edge where the coupling between the electrons and the external field is effective. Therefore, the amplitude mode exists even when the superconductor is relatively clean, but its contribution to the response function is small. These behaviors, which are qualitatively consistent with the experimental results, are obtained by taking into account the static field nonperturbatively.