Microwave conductivity in the ferropnictides with specific application to Ba$_{1-x}$K$_x$Fe$_2$As$_2$

Abstract

We calculate the microwave conductivity of a two band superconductor with $s^\pm$ gap symmetry. Inelastic scattering is included approximately in a BCS model augmented by a temperature dependent quasiparticle scattering rate assumed, however, to be frequency independent. The possibility that the s-wave gap on one or the other of the electron or hole pockets is anisotropic is explored including cases with and without gap nodes on the Fermi surface. A comparison of our BCS results with those obtained in the Two Fluid Model (TFM) is provided as well as with the case of the cuprates where the gap has d-wave symmetry and with experimental results in Ba$_{1-x}$K$_x$Fe$_2$As$_2$. The presently available microwave conductivity data in this material provides strong evidence for large anisotropies in the electron pocket s-wave gap. While a best fit favors a gap with nodes on the Fermi surface this disagrees with some but not all penetration depth measurements which would favor a node-less gap as do also thermal conductivity and nuclear magnetic resonance data.