Dopant Clustering, Electronic Inhomogeneity, and Vortex Pinning in Iron-Based Superconductors

We use scanning tunneling microscopy to map the surface structure, nanoscale electronic inhomogeneity, and vitreous vortex phase in the hole-doped superconductor Sr\(_{0.75}\)K\(_{0.25}\)Fe\(_2\)As\(_2\) with \(T_c\)=32 K. We find the low-\(T\) cleaved surface is dominated by a half-Sr/K termination with \(1\times 2\) ordering and ubiquitous superconducting gap, while patches of gapless, unreconstructed As termination appear rarely. The superconducting gap varies by \(\sigma/\bar{\Delta}\)=16% on a \(\sim\)3 nm length scale, with average \(2\bar{\Delta}/k_B T_c=3.6\) in the weak coupling limit. The vortex core size provides a measure of the superconducting coherence length \(\xi\)=2.3 nm. We quantify the vortex lattice correlation length at 9 T in comparison to several iron-based superconductors. The comparison leads us to suggest the importance of dopant size mismatch as a cause of dopant clustering, electronic inhomogeneity, and strong vortex pinning.