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Microwave response of superconductors with paramagnetic impurities

Mehdi Zarea* and J. A. Sauls†

  • *Contact author: zarea.mehdi@gmail.com
  • †Contact author: sauls@lsu.edu
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Phys. Rev. B 114, 214505 – Published 8 October, 2026

DOI: https://doi.org/10.1103/tkw2-2njr

Abstract

We develop theoretical methods to predict the effects of paramagnetic impurities on the microwave response of conventional spin-singlet superconductors. Our focus is on superconducting devices and resonators with low concentrations of impurities and exchange interactions with conduction electrons. We connect the subgap quasiparticle spectrum generated by pair-breaking to the frequency and temperature dependence of the conductivity for superconductors operating at microwave frequencies. We report theoretical results for superconducting device performance—dissipation, quality factor, and frequency-shift anomalies—based on self-consistent calculations of the current response and penetration of the electromagnetic field at the vacuum-superconducting interface. Key results include the prediction of a nonmonotonic anomaly in the low-frequency superfluid fraction and penetration depth at very low temperatures related to the subgap quasiparticle spectrum. Dissipation of microwave power is predicted from intra- and interimpurity band transitions at GHz frequencies at low temperatures, including a physical mechanism responsible for residual resistance. We predict anomalies in the resonant frequency, f(T), and quality factor, Q(T), of high-Q SRF cavities operating in the GHz range at low temperatures that are sensitive to nonmagnetic and paramagnetic impurity disorder.

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Phys. Rev. B 114, 214505– Published 8 October, 2026
  • Received 23 December 2025
  • Accepted 15 September 2026
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Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article's title, journal citation, and DOI.

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