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

Takayuki Kubo

doi:10.1103/PhysRevApplied.17.014018

paper

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

arXiv:2110.00573 · doi:10.1103/PhysRevApplied.17.014018

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 $R_{s}$ , 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 ( $γ / Δ_{0} \sim 1$ ) minimizes $R_{s}$ . Here, $Δ_{0}$ is the pair potential for the idealized ( $Γ \to 0$ ) superconductor for the temperature $T \to 0$ . We find the optimum $Γ$ can also reduce $R_{s}$ by one order of magnitude for a clean superconductor ( $γ / Δ_{0} < 1$ ) and a few tens $%$ for a dirty superconductor ( $γ / Δ_{0} > 1$ ). Also, we find a nearly-ideal ( $Γ/ Δ_{0} ≪ 1$ ) clean-limit superconductor exhibits a frequency-independent $R_{s}$ 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 $R_{s}$ obeys the $ω^{2}$ dependence. The subgap-state-induced residual surface resistance $R_{res}$ 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 $J_{d}$ .

15 pages, 15 figures

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

Abstract

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