The Mattis-Bardeen theory is extended by introducing the complex number of the superconducting gap energy, by which BCS density of states is broadened and the small density of quasiparticle states that appears in the energy gap is well predicted. Using the extended Mattis-Bardeen theory, the surface resistance of superconductors and quality factors of superconducting resonators are calculated. It is shown that simulated temperature dependence of quality factors of superconducting resonators agree very well with the measured ones. It is also demonstrated that the calculated residual quasiparticle number of a superconducting resonator using the density of states consisting of the gap-broadened and localized quasiparticle states agrees quantitatively with the measured one.
- density of states
- surface resistance