Effects of nonmagnetic impurities and subgap states on the kinetic inductance, complex conductivity, quality factor and depairing current density

Abstract

We investigate how a combination of a nonmagnetic-impurity scattering rate γ and finite subgap states parametrized by Dynes Γ affects various physical quantities relevant to to superconducting devices: kinetic inductance L k , complex conductivity σ, surface resistance Rs, quality factor Q, and depairing current density J d . All the calculations are based on the Eilenberger formalism of the BCS theory. We assume the device materials are extreme type-II s-wave superconductors. It is well known that the optimum impurity concentration (γ/∆0 ∼ 1) minimizes Rs. Here, ∆0 is the pair potential for the idealized (Γ → 0) superconductor for the temperature T → 0. We find the optimum Γ can also reduce Rs by one order of magnitude for a clean superconductor (γ/∆0 < 1) and a few tens % for a dirty superconductor (γ/∆0 > 1). Also, we find a nearly-ideal (Γ/∆0 ≪ 1) clean-limit superconductor exhibits a frequency-independent Rs for a broad range of frequency ω, which can significantly improve Q of a very compact cavity with a few tens of GHz frequency. As Γ or γ increases, the plateau disappears, and Rs obeys the ω 2 dependence. The subgap-state-induced residual surface resistance Rres is also studied, which can be detected by an SRF-grade high-Q 3D resonator. We calculate L k (γ, Γ, T ) and J d (γ, Γ, T ), which are monotonic increasing and decreasing functions of (γ, Γ, T ), respectively. Measurements of (γ, Γ) of device materials can give helpful information on engineering (γ, Γ) via materials processing, by which it would be possible to improve Q, engineer L k , and ameliorate J d .