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 $\sigma \mathrm{/}\bar{\mathrm{\Delta }}$=16% on a $\sim$3 nm length scale, with average $2\bar{\mathrm{\Delta }}\mathrm{/}{k}_B{T}_c=3.6$ 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.