For solid-solution ${\mathrm{Ba}}_{1-x}{\mathrm{K}}_x{\mathrm{Fe}}_2{\mathrm{As}}_2$ Fermi surface evolution is mapped via Bloch spectral functions calculated using density functional theory implemented in Korringa-Kohn-Rostoker multiple scattering theory with the coherent-potential approximation. Spectral functions reveal electronic dispersion, topology, orbital character, and broadening (electron-lifetime effects) due to chemical disorder. Dissolution of electron cylinders occurs near $x\sim 0.9$ with a nonuniform, topological (Lifshitz) transition, reducing the interband interactions; yet the dispersion maintains its $d_{xz}$ or $d_{yz}$ character. Formation energies indicate alloying at $x=0.35$, as observed, and a tendency for segregation on the K-rich ($x>0.6$) side, explaining the difficulty of controlling sample quality and the conflicting results between characterized electronic structures. Our results reveal Fermi surface transitions in alloyed samples that influence $s^{\pm }$ to nodal superconductivity and suggest the origin for deviations of common trends in Fe-based superconductors, such as Bud’ko-Ni-Canfield scaling.

• Received 11 November 2013

DOI:https://doi.org/10.1103/PhysRevLett.112.156401