A model of superconducting rf dissipation from Bogoliubov quasiparticles in a modified two-fluid framework

Investigating Nb surface treatments to optimize superconducting rf (SRF) applications revealed a peculiar trend in certain Nb SRF cavities: a quality factor that increases as a function of field, referred to as an "anti-Q slope". Specifically referring to the temperature-dependent component of the surface resistance decreasing with field strength, this curious behavior is not captured in long-established theories quantifying SRF dissipation. We present a simple yet effective theoretical framework that is successful in not only producing an anti-Q slope, we also include a proposed mechanism on how to turn the anti-Q slope on and off. By numerically solving the Bogoliubov-de Gennes self-consistent field equations for a superconducting surface in a parallel AC magnetic field, we compute density profiles using a two-fluid framework to characterize the underlying single-particle excitations and condensed pairs responding to an oscillating field. Surface resistances are calculated from Ohmic dissipation in a semi-classical theory of conductivity, and this analysis is combined with complementary density-functional theory (DFT) calculations to quantify realistic elastic scattering times of electrons interacting with impurities in Nb. Finally, we show the temperature and frequency dependencies of this new model agree well with established theories of SRF dissipation.