Electromagnetic response of disordered superconducting cavities

Abstract

We present the results for the resonant frequency shift and quality factor of disordered niobium (Nb) superconducting radio-frequency cavities driven out of equilibrium by the resonant microwave field. The theory is based on the non-equilibrium 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 fractions of kHz over the full temperature range 0 < T ≤ Tc, including the negative frequency shift anomalies that are observed very near Tc. 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→Tc−. An analytical approximation to the full current response, valid for |T − Tc|≪ Tc, accounts for the negative frequency shift near Tc. 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.