Pairing mechanism for nodal $s$-wave superconductivity in BaFe${}_2$(As,P)${}_2$: Analysis beyond Migdal-Eliashberg formalism

Abstract

The pairing mechanism and gap structure in Ba122 pnictides have been hotly discussed for long time as one of the central issues in Fe-based superconductors. Here, we attack this problem by taking account of the vertex corrections (VCs) for the Coulomb interaction $U$ ($U$-VCs), which are totally dropped in conventional Migdal-Eliashberg formalism. The $U$-VC in the charge susceptibility induces strong orbital fluctuations, and the $U$-VC also enlarges the orbital-fluctuation-mediated attractive interaction. By analyzing the effective multiorbital Hubbard model for Ba122 pnictides, we find that the orbital fluctuations develop in all four $d$-orbitals ($t_{2g}$- and $z^2$-orbitals), by which the FSs are composed. For this reason, nearly isotropic gap function appears on all the hole-type FSs, including the outer hole-FS around Z-point composed of $z^2$-orbital. In contrast, nodal gap structure appears on the electron-type FSs for wide parameter range. The obtained nodal $s$-wave state changes to fully-gapped $s$-wave state without sign-reversal ($s_{++}$-wave state) by introducing small amount of impurities, accompanied by small reduction in $T_c$. The present microscopic theory naturally explains the important characteristics of the gap structure of both hole- and electron-FSs in Ba122 pnictides, without introducing any phenomenological pairing interaction.

12 pages, 13 figures, to be published in Phys. Rev. B

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• Superconducting Order Parameter and Bosonic Mode in Hydrogen-Substituted NdFeAsO${}_{0.6}$H${}_{0.36}$ Revealed by Multiple Andreev Reflection Spectroscopy
• Superconducting Order Parameters in overdoped BaFe${}_{1.86}$Ni${}_{0.14}$As${}_2$ Revealed by Multiple Andreev Reflection Spectroscopy of Planar Break-Junctions