The Anomalous Resonant Frequency Variation of Microwave Superconducting Niobium Cavities Near $T_c$

Superconducting radio-frequency (SRF) niobium cavities are the modern means of particle acceleration and an enabling technology for record coherence superconducting quantum systems and ultra-sensitive searches for new physics. Here we report a systematic effect observed on a large set of bulk SRF cavities - an anomalous decrease of the resonant frequency at temperatures just below the superconducting transition temperature - which opens up a new means of understanding the physics behind nitrogen doping and other modern cavity surface treatments relevant for future quality factor and coherence improvements. The magnitude of the frequency change correlates systematically with the near-surface impurity distribution in studied cavities and with the observed $T_c$ variation. We also present the first demonstration of the coherence peak in the real part of the AC complex conductivity in Nb SRF cavities and show that its magnitude varies with impurity distribution.