Electromagnetic Response of Disordered Superconducting Cavities

We present theoretical predictions for the resonance frequency and quality factor of disordered Nb SRF cavities driven out of equilibrium by the microwave field [1,2]. We are able to predict the observed frequency shifts with a precision of order fractions of a kHz over the full temperature range 0 < T ≤ T_c , including the negative frequency shift anomalies that are observed very near T_c [3]. The quality factor, Q, of these cavities shows non-monotonic behavior as a function of the mean quasiparticle scattering time τ. The maximum of the quality factor is related to the pair-breaking effect of disorder on the superfluid fraction for τ≈h/(2π)² k_BT_c. The minimum Q occurs for in the clean limit and for ωτ ≈1. This behavior is explained by the interplay between London penetration depth and the a.c resistance in the superconducting state. We also include results for the residual resistance which reduces the quality factor and frequency shift, and also leads to a wider temperature range of negative frequency shift.

[1] Zarea M, Ueki H and Sauls J.A (2023), Front. Electron. Mater. 3:1259401. doi: 10.3389/femat.2023.1259401

[2] Ueki H, Zarea M and Sauls J. A (2022), arXiv:2207.14236, https://doi.org/10.48550/arXiv.2207.14236

[3] Bafia et al (2021),e-print arXiv:2103.10601, https://doi.org/10.48550/arXiv.2103.10601