Microwave Surface-Impedance Measurements of the Magnetic Penetration Depth in Single Crystal Ba1-xKxFe2As2 Superconductors: Evidence for a Disorder-Dependent Superfluid Density

We report high-sensitivity microwave measurements of the in-plane penetration depth $\lambda_{ab}$ and quasiparticle scattering rate $1/\tau$ in several single crystals of hole-doped Fe-based superconductor Ba$_{1-x}$K$_x$Fe$_2$As$_2$ ($x\approx 0.55$). While power-law temperature dependence of $\lambda_{ab}$ with the power $\sim 2$ is found in crystals with large $1/\tau$, we observe exponential temperature dependence of superfluid density consistent with the existence of fully opened two gaps in the cleanest crystal we studied. The difference may be a consequence of different level of disorder inherent in the crystals. We also find a linear relation between the low-temperature scattering rate and the density of quasiparticles, which shows a clear contrast to the case of d-wave cuprate superconductors with nodes in the gap. These results demonstrate intrinsically nodeless order parameters in the Fe-arsenides.