Spectroscopic and thermodynamic properties in a four-band model for pnictides

In this paper we provide a comprehesive analysis of different properties of pnictides both in the normal and superconducting state, with a particular focus on the optimally-doped Ba$_{1-x}$K$_{x}$Fe$_2$As$_2$ system. We show that, by using the band dispersions experimentally measured by ARPES, a four-band Eliashberg model in the intermediate-coupling regime can account for both the measured hierarchy of the gaps and for several spectroscopic and thermodynamic signatures of low-energy renormalization. These include the kinks in the band dispersion and the effective masses determined via specific-heat and superfluid-density measurements. We also show that, although an intermediate-coupling Eliashberg approach is needed to account for the magnitude of the gaps, the temperature behavior of the thermodynamic quantities does not show in this regime a significant deviation with respect to weak-coupling BCS calculations. This can explain the apparent success of two-band BCS fits of experimental data reported often in the literature.