  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.
