We report combined experimental and theoretical analysis of superconductivity in CaK(Fe$_{1-x}$Ni$_x$)$_4$As$_4$ (CaK1144) for $x=$0, 0.017 and 0.034. To obtain the superfluid density, $rho=left(1+Delta lambda_L(T)/lambda_L(0) right)^{-2}$, the tempe
rature dependence of the London penetration depth, $Delta lambda_L (T)$, was measured by using tunnel-diode resonator (TDR) and the results agreed with the microwave coplanar resonator (MWR) with the small differences accounted for by considering a three orders of magnitude higher frequency of MWR. The absolute value of $lambda_L (T ll T_c) approx lambda_L(0)$ was measured by using MWR, $lambda_L (mathrm{5~K}) approx 170 pm 20$ nm, which agreed well with the NV-centers in diamond optical magnetometry that gave $lambda_L (mathrm{5~K}) approx 196 pm 12$ nm. The experimental results are analyzed within the Eliashberg theory, showing that the superconductivity of CaK1144 is well described by the nodeless s$_{pm}$ order parameter and that upon Ni doping the interband interaction increases.
Most iron-based superconductors are characterized by the s+- symmetry of their order parameter, and are expected to go through a transition to the s++ state if enough disorder is introduced. We previously reported the observation of this transition i
n Ba(Fe1-xRhx)2As2 through a study of the disorder dependence of the critical temperature and low-temperature London penetration depth. In this paper we report on the analysis of the electrodynamic response of the same sample across the transition and we identify peculiarities in the behaviour of the surface resistance and normal conductivity, that can be considered as traces of the transition itself.
