Electromagnetic Response of Disordered Superconducting Cavities

TL;DR

This paper investigates how disorder affects the electromagnetic response of superconducting cavities, accurately predicting frequency shifts and quality factor variations near the critical temperature using a nonequilibrium superconductivity theory.

Contribution

It introduces a theoretical framework that predicts the electromagnetic response of disordered superconducting cavities, including negative frequency shifts near T_c, with high precision.

Findings

Accurate prediction of frequency shifts within a few Hz across temperature range.

Identification of the origin of negative frequency shifts as a competition between skin depth and penetration depth.

Analysis of the non-monotonic quality factor dependence on disorder and quasiparticle scattering.

Abstract

We present results for the resonant frequency shift and quality factor of disordered Nb SRF cavities driven out of equilibrium by the resonant microwave field. The theory is based on the nonequilibrium theory of superconductivity for the current response to the electromagnetic field at the vacuum-metal interface. We are able to accurately predict the observed frequency shifts with a precision of order several Hz over the full temperature range $0 < T \le T_c$, including the negative frequency shift anomalies that are observed very near $T_c$. The origin of these anomalies is shown to be the competition between the normal metal skin depth and the London penetration depth which diverges as $T\rightarrow T_c^-$. An analytic approximation to the full current response, valid for $|T-T_c|\ll T_c$, accounts for the negative frequency shift near $T_c$. The non-monotonic dependence of the quality factor on the quasiparticle scattering rate is related to the pair-breaking effect of disorder on the superfluid fraction, and thus the London penetration depth.