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Local inhomogeneity and filamentary superconductivity in Pr-doped CaFe$_{2}$As$_{2}$

We use multi-scale techniques to determine the extent of local inhomogeneity and superconductivity in Ca$_{0.86}$Pr$_{0.14}$Fe$_{2}$As$_{2}$ single crystal. The inhomogeneity is manifested as a spatial variation of praseodymium concentration, local density of states, and superconducting order parameter. We show that the high-$T_{c}$ superconductivity emerges from clover-like defects associated with Pr dopants. The highest $T_{c}$ is observed in both the tetragonal and collapsed tetragonal phases, and its filamentary nature is a consequence of non-uniform Pr distribution that develops localized, isolated superconducting regions within the crystals.