Phenomenology of CaKFe4As4 explained in the framework of four bands Eliashberg theory

Recent angle-resolved photoemission spectroscopy measurements of CaKFe4As 4 report the presence of four superconductive gaps on different sheets of Fermi surface. The interesting aspect of this supercon- ductor is that it is stoichiometric and with a high critical temperature. I show that the phenomenology of this superconductor can be explained in the framework of four-band s ±-wave Eliashberg theory choosing antiferromagnetic spin fluctuations as pairing glue. In particular, various experimental data reported in literature: the energy gaps, the critical temperature, the temperature dependence of the upper critical field, the penetration depth and the thermopower can be reproduced by this model in a strong-coupling regime with a small number of free parameters.