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We report on the dramatic effect of random point defects, produced by protonirradiation, on the superfluid density $\rho_{s}$ in superconductingCa$_{0.5}$Na$_{0.5}$Fe$_2$As$_2$ single crystals. The magnitude of thesuppression is inferred from measurements of the temperature-dependent magneticpenetration depth $\lambda(T)$ using magnetic force microscopy. Our findingsindicate that a radiation dose of 2$\times10^{16}$cm$^{-2}$ produced by 3 MeVprotons results in a reduction of the superconducting critical temperature$T_{c}$ by approximately 10%. % with no appreciable change in the slope of theupper critical fields. In contrast, $\rho_{s}(0)$ is suppressed byapproximately 60%. This break-down of the Abrikosov-Gorkov theory may beexplained by the so-called "Swiss cheese model", which accounts for the spatialsuppression of the order parameter near point defects similar to holes in Swisscheese. Both the slope of the upper critical field and the penetration depth$\lambda(T/T_{c})/\lambda(0)$ exhibit similar temperature dependences beforeand after irradiation. This may be due to a combination of the highlydisordered nature of Ca$_{0.5}$Na$_{0.5}$Fe$_2$As$_2$ with large intraband andsimultaneous interband scattering as well as the $s^\pm$-wave nature of shortcoherence length superconductivity.

physical review. b, condensed matter and materials physics

Magnetic penetration-depth measurements of a suppressed superfluid  density of superconducting Ca$_{0.5}$Na$_{0.5}$Fe$_2$As$_2$ single crystals  by proton irradiation