Low temperature dissipative conductivity of superconductors with paramagnetic impurities

In s-wave superconductors containing a low concentration of localized magnetic impurities, the only electronic excitations that remain available at low temperatures are associated with excitations of the localized spins. We propose a new mechanism for interaction between electromagnetic fields and localized spins in the superconductors. Supercurrents in disordered superconductors generate sample-specific spatial fluctuations of the itinerant-electron spin density, which act as an exchange field on the localized spins. An ac electric field of frequency ω accelerates the supercurrent and thereby drives a strong, time-dependent exchange field. The resulting spin–electromagnetic coupling scales as 1/ω and greatly exceeds the direct Zeeman coupling to the magnetic field of the electromagnetic wave. We show that the dissipative conductivity saturates to a finite value in the low-frequency limit. Using the fluctuation-dissipation theorem, we further evaluate the equilibrium current-noise spectrum arising from fluctuations of the spin subsystem.