Superconductivity on the Verge of a Pressure-Induced Lifshitz Transition in CaFe2As2: an Interpretation Within the Eliashberg Theory

In a recent paper, we presented the first directional point-contact Andreev reflection spectroscopy (PCARS) measurements on CaFe2As2 crystals under quasi-hydrostatic pressure and discussed the pressure dependence of the gaps and the critical temperature. While Tc exhibits a well-known smooth dependence and a broad maximum at about 0.6 GPa, both gaps increase very sharply in a small pressure range between 0.5 and 0.6 GPa, leading to a doubling of the ratio 2D2/kBTc and a quadruplication of the ratio 2D1/kBTc, D1 and D2 being the small and large gap, respectively. This peculiar behavior is likely to be related to a sharp change in the lattice structure that, in turn, produces a 2D-3D topological transition in the hole-like Fermi surface sheet. In this work, we show that, within an effective three-band Eliashberg theory for the electron-spin fluctuation coupling (s± symmetry), these results can be rationalized as being due to a large increase of the electron-boson coupling, which mimics the effects of a boost mechanism for the coupling related to the underlying Lifshitz transition.