Fitting of Bardeen-Cooper-Schrieffer theory to measured microwave conductivity of ${\mathrm{YBa}}_2$${\mathrm{Cu}}_3$${\mathrm{O}}_7$ films

The weak-coupling BCS expression for the complex conductivity, in the local limit and with a finite carrier mean free path l, is fitted to data from recent experiments that accurately measured both the real and imaginary parts of the microwave (58.9-GHz) conductivity on thin ${\mathrm{YBa}}_2$ ${\mathrm{Cu}}_3$ ${\mathrm{O}}_7$ films. The fitting, for temperatures up to a few degrees below ${\mathit{T}}_{\mathit{c}}$, is achieved by adjusting the temperature dependence of the l and of the effective mass, within a model for a pure superconductor. Just below ${\mathit{T}}_{\mathit{c}}$, an effective-medium model is invoked to describe a mixture of superconducting- and normal-state regions. This phenomenological procedure fits, in particular, the narrow peak that was measured in the real part of the conductivity near ${\mathit{T}}_{\mathit{c}}$.