A phenomenological multiband Eliashberg model for LiFeAs

The phenomenology of LiFeAs superconductor can be explained in the framework of a four-band s$\pm$-wave Eliashberg theory. We have examined the experimental data available in literature and we have found out that it is possible to reproduce the experimental critical temperature, the gap values and the upper critical magnetic field within an effective model in moderate strong-coupling regime that must include both an intraband term $\lambda_{11}\sim0.9$ and an interband spin-fluctuations ($\lambda_{tot}^{sf}\sim1.5$) coupling. The presence of a non negligible intraband coupling can be a fictitious effect of the violation of Migdal's Theorem.