Surface impedance of superconductors with magnetic impurities

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.

9 pages, 3 figs; v2: published version

References in corpus (5)

• Superheating field of superconductors within Ginzburg-Landau theory
• Temperature dependence of the superheating field for superconductors in the high-k London limit
• Tunneling study of cavity grade Nb: possible magnetic scattering at the surface
• Surface impedance of superconductors with weak magnetic impurities
• Statistics of subgap states in $s_{\pm }$ superconductors

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• A low energy muon spin rotation and point contact tunneling study of niobium films prepared for superconducting cavities
• Microscopic theory of supercurrent suppression by gate-controlled surface depairing
• Tuning critical field, critical current, and diode effect of narrow thin-film superconductors through engineering inhomogeneous Pearl length
• Local impedance on a rough surface of a chiral $p$-wave superconductor
• Microscopic Examination of SRF-quality Nb Films through Local Nonlinear Microwave Response
• Depth-resolved Characterization of Meissner Screening Breakdown in Surface Treated Niobium
• Local Limit Disorder Characteristics of Superconducting Radio Frequency Cavities