The influence of antiferromagnetism, soft out-of plane phonons and heavy electrons on the superconducting pairing mechanism of Ba1-xKxFe2As2

Based on ab-initio calculated parameters, we apply a theoretical model on the iron-based BaFe2As2 superconductor that takes into account dramatic enhancements of the electron-phonon coupling of soft transverse phonons in the FeAs layers and antiferromagnetism. Our model is able to reproduce the Tc values of BaFe2As2 found under pressure in experiments. To calculate the Tc of the K-doped Ba1-xKxFe2As2 system as a function of the K content, we additionally consider the experimentally observed effective mass enhancements and Kondo temperatures in the strongly over-doped region (0.8 < x < 1), which decouple the antiferromagnetism and electron-phonon scattering. The highest theoretical Tc at the optimal doping concentration is reproduced after optimization of antiferromagnetic fluctuations and electron-phonon coupling. Our model is also able to reproduce the dip-like structure in Tc in the region where a re-entrant tetragonal phase of C4 symmetry is found (0.24 < x < 0.28) and indicates the weakening effect of local exchange correlation energy as responsible for Tc reduction. Our model thus demonstrates that the high transition temperatures and the exact doping and pressure dependence of this iron-based superconductor can be explained within an extended electron-phonon coupling model in which the structural, magnetic and electronic degrees of freedom are strongly intertwined.