Effects of Nonmagnetic Impurities and Subgap States on the Kinetic Inductance, Complex Conductivity, Quality Factor, and Depairing Current Density

We investigate how a combination of a nonmagnetic impurity scattering rate gamma and finite subgap states parametrized by Dynes F affects various physical quantities relevant to superconducting devices made from extreme type-II s-wave superconductors. All the calculations are based on the Eilenberger formalism of the BCS theory. It is well known that the optimum impurity concentration minimizes the surface resistance Rs. We find the optimum F can also reduce Rs by one order of magnitude for a clean superconductor (gamma /A0 1) and a few tens of % for a dirty superconductor (gamma /A0 1). Here, A0 is the pair potential for the idealized (F -> 0) BCS superconductor for T -> 0. Also, we find a nearly ideal (F/A0 << 1) cleanlimit superconductor exhibits a frequency-independent Rs for a broad range of frequency w, which can significantly improve Q of a compact cavity with a few tens of GHz frequency. As F or gamma increases, Rs obeys the w2 dependence. The subgap-state-induced residual surface resistance Rres is also studied, which can be detected by a high-Q three-dimensional resonator. We calculate the kinetic inductance Lk(gamma , F, T) and the depairing current density Jd(gamma ,F, T), which are monotonic increasing and decreasing functions of (gamma , F, T), respectively. Measurements of (gamma , F) of device materials can give helpful information on improving Q, engineering Lk, and ameliorating Jd via materials processing.