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.
While unusual normal state properties, such as non-Fermi liquid behavior of the resistivity, are commonly associated with strong quantum fluctuations, evidence for its presence inside the superconducting dome are much scarcer. In this paper, we use s
ensitive and minimally invasive optical magnetometry based on NV-centers in diamond to probe the doping evolution of the $T=0$ penetration depth in the electron-doped iron-based superconductor Ba(Fe$_{1-x}$Co$_x$)$_2$As$_2$. A non-monotonic evolution with a pronounced peak in the vicinity of the putative magnetic QPT is found. This behavior is reminiscent to that previously seen in isovalently-substituted BaFe$_2$(As$_{1-x}$P$_x$)$_2$ compounds, despite the notable differences between these two systems. Whereas the latter is a very clean system that displays nodal superconductivity and a single simultaneous first-order nematic-magnetic transition above, and even somewhat below, $T_c$, the former is a significantly dirtier system with fully gapped superconductivity and split second-order nematic and magnetic transition above $T_c$. Thus our observation that such distinct systems display remarkably similar penetration depth peaks, combined with the theoretical result that a QPT alone does not ensure the existence of a peak, unveils a puzzling and seemingly universal manifestation of quantum fluctuations in the iron pnictides.
Non-invasive magnetic field sensing using optically - detected magnetic resonance of nitrogen-vacancy (NV) centers in diamond was used to study spatial distribution of the magnetic induction upon penetration and expulsion of weak magnetic fields in s
everal representative superconductors. Vector magnetic fields were measured on the surface of conventional, Pb and Nb, and unconventional, LuNi$_2$B$_2$C, Ba$_{0.6}$K$_{0.4}$Fe$_2$As$_2$, Ba(Fe$_{0.93}$Co$_{0.07}$)$_2$As$_2$, and CaKFe$_4$As$_4$, superconductors, with diffraction - limited spatial resolution using variable - temperature confocal system. Magnetic induction profiles across the crystal edges were measured in zero-field-cooled (ZFC) and field-cooled (FC) conditions. While all superconductors show nearly perfect screening of magnetic fields applied after cooling to temperatures well below the superconducting transition, $T_c$, a range of very different behaviors was observed for Meissner expulsion upon cooling in static magnetic field from above $T_c$. Substantial conventional Meissner expulsion is found in LuNi$_2$B$_2$C, paramagnetic Meissner effect (PME) is found in Nb, and virtually no expulsion is observed in iron-based superconductors. In all cases, good correlation with macroscopic measurements of total magnetic moment is found. Our measurements of the spatial distribution of magnetic induction provide insight into microscopic physics of the Meissner effect.
