Surface impedance of superconductors with magnetic impurities

TL;DR

This paper develops a microscopic theory for the surface impedance of s-wave superconductors with magnetic impurities, explaining residual resistance in SRF cavities through analytical and numerical results across various conditions.

Contribution

It introduces a comprehensive microscopic framework for understanding how magnetic impurities affect the surface impedance of superconductors, applicable to SRF cavities and qubits.

Findings

Surface resistance saturates at zero temperature in gapless superconductivity.

Magnetic impurities cause residual resistance in superconducting surfaces.

The theory applies across a wide range of parameters, enabling experimental comparisons.

Abstract

Motivated by the problem of the residual surface resistance of the superconducting radio-frequency (SRF) cavities, we develop a microscopic theory of the surface impedance of s-wave superconductors with magnetic impurities. We analytically calculate the current response function and surface impedance for a sample with spatially uniform distribution of impurities, treating magnetic impurities in the framework of the Shiba theory. The obtained general expressions hold in a wide range of parameter values, such as temperature, frequency, mean free path, and exchange coupling strength. This generality, on the one hand, allows for direct numerical implementation of our results to describe experimental systems (SRF cavities, superconducting qubits) under various practically relevant conditions. On the other hand, explicit analytical expressions can be obtained in a number of limiting cases, which makes possible further theoretical investigation of certain regimes. As a feature of key relevance to SRF cavities, we show that in the regime of "gapless superconductivity" the surface resistance exhibits saturation at zero temperature. Our theory thus explicitly demonstrates that magnetic impurities, presumably contained in the oxide surface layer of the SRF cavities, provide a microscopic mechanism for the residual resistance.