The superconducting properties of LaFeAsO$_{1-x}$F$_{x}$ in conditions of optimal electron-doping are investigated upon the application of external pressure up to $sim 23$ kbar. Measurements of muon-spin spectroscopy and dc magnetometry evidence a cl
ear mutual independence between the critical temperature $T_{c}$ and the low-temperature saturation value for the ratio $n_{s}/m^{*}$ (superfluid density over effective band mass of Cooper pairs). Remarkably, a dramatic increase of $sim 30$ % is reported for $n_{s}/m^{*}$ at the maximum pressure value while $T_{c}$ is substantially unaffected in the whole accessed experimental window. We argue and demonstrate that the explanation for the observed results must take the effect of non-magnetic impurities on multi-band superconductivity into account. In particular, the unique possibility to modify the ratio between intra-band and inter-bands scattering rates by acting on structural parameters while keeping the amount of chemical disorder constant is a striking result of our proposed model.
The effect of hydrostatic pressure and partial Na substitution on the normal-state properties and the superconducting transition temperature ($T_c$) of K$_{1-x}$Na$_x$Fe$_2$As$_2$ single crystals were investigated. It was found that a partial Na subs
titution leads to a deviation from the standard $T^2$ Fermi-liquid behavior in the temperature dependence of the normal-state resistivity. It was demonstrated that non-Fermi liquid like behavior of the resistivity for K$_{1-x}$Na$_{x}$Fe$_2$As$_2$ and some KFe$_2$As$_2$ samples can be explained by disorder effect in the multiband system with rather different quasiparticle effective masses. Concerning the superconducting state our data support the presence of a shallow minimum around 2 GPa in the pressure dependence of $T_c$ for stoichiometric KFe$_2$As$_2$. The analysis of $T_c$ in the K$_{1-x}$Na$_{x}$Fe$_2$As$_2$ at pressures below 1.5 GPa showed, that the reduction of $T_c$ with Na substitution follows the Abrikosov-Gorkov law with the critical temperature $T_{c0}$ of the clean system (without pair-breaking) which linearly depends on the pressure. Our observations, also, suggest that $T_c$ of K$_{1-x}$Na$_x$Fe$_2$As$_2$ is nearly independent of the lattice compression produced by the Na substitution. Further, we theoretically analyzed the behavior of the band structure under pressure within the generalized gradient approximation (GGA). A qualitative agreement between the calculated and the recently in de Haas-van Alphen experiments [T. Terashima et al., Phys.Rev.B89, 134520(2014)] measured pressure dependencies of the Fermi-surface cross-sections has been found. These calculations, also, indicate that the observed minimum around 2~GPa in the pressure dependence of $T_c$ may occur without a change of the pairing symmetry.
