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Low-temperature dissipative conductivity of superconductors with paramagnetic impurities

Shiang-Bin Chiu1,*, Anton Andreev1, Alexander Burin2, and Boris Z. Spivak1

  • *Contact author: sbinchiu@uw.edu
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Phys. Rev. Research 8, 033317 – Published 15 September, 2026

DOI: https://doi.org/10.1103/bc3f-kpsj

Abstract

In s-wave superconductors with a small concentration of magnetic impurities, the only electronic excitations that remain available at low temperatures are the excitations of the system of localized spins. We discuss a mechanism of interaction between electromagnetic waves and the localized spins in disordered superconductors. A supercurrent induces randomly distributed spin density of the itinerant electrons, which couples to the impurity spins by exchange interaction. Acceleration of the Cooper pair condensate by the external ac electric field of frequency ω creates a strong, time-dependent exchange field acting on the localized spins, which is inversely proportional to ω. As a result, at low frequencies the dissipative conductivity saturates to a nonzero value. We also predict that, in the presence of a dc magnetic field parallel to the superconducting film, the system exhibits a large positive magnetoconductance. Using the fluctuation-dissipation theorem, we evaluate the spectrum of equilibrium current fluctuations induced by the spin fluctuations.

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Phys. Rev. Research 8, 033317– Published 15 September, 2026
  • Received 23 December 2025
  • Revised 21 April 2026
  • Accepted 10 August 2026
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