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 <italic>T</italic>_{<italic>c</italic>} 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 2Δ₂/<italic>k</italic>_{<italic>B</italic>}<italic>T</italic>_{<italic>c</italic>} and a quadruplication of the ratio 2Δ₁/<italic>k</italic>_{<italic>B</italic>}<italic>T</italic>_{<italic>c</italic>}, Δ₁ and Δ₂ 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 (<italic>s</italic>± 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. [ABSTRACT FROM AUTHOR]