Determination of the Bardeen–Cooper–Schrieffer material parameters of the HIE-ISOLDE superconducting resonator

Abstract

Superconducting material parameters of the Nb film coatings on the quarter-wave resonator for the HIE-ISOLDE project were studied by fitting experimental results with the Bardeen–Cooper–Schrieffer Mattis–Bardeen (BCS-MB) theory. We pointed out a strong correlation among fitted estimators of material parameters in the BCS-MB theory, and used a procedure to reduce the uncertainty by merging two χ2 distributions of the surface resistance and effective penetration depth. In this procedure, unlike previous studies, BCS coherence length (ξ0) and London penetration depth (λL) were not fixed at their literature values in the calculation because in our film, whose thickness is from 2 to 13 μm, they may take altered values as a consequence of microstructual defects. Since surface resistance and penetration depth have similar dependencies on coherence length and mean free path, the effects of the correlation between the estimators of these two parameters could not be mitigated by just combining surface resistance and penetration depth data. We used upper critical field measurement by SQUID magnetometry to provide a complementary constraint to these RF measurements, and this allowed all the material parameters to be obtained by fitting the experimental data. In the best performing cavity, the determined parameters are ξ0 = 29 nm, λL = 26 nm, mean free path l = 99 nm, and coupling strength Δ0/kBTc = 1.7. The coherence length is slightly shorter than for clean bulk Nb (39 nm) in the literature although the Nb film is thick and rather bulk-like. A poorly performing cavity showed weaker coupling constant Δ0/kBTc = 1.5 which may indicate film contamination during the coating process.