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

TL;DR

This paper investigates the pairing mechanism in BaFe2(As,P)2 superconductors by including vertex corrections beyond Migdal-Eliashberg theory, revealing orbital fluctuation-driven pairing and explaining the observed gap structures.

Contribution

It introduces a microscopic theory incorporating vertex corrections, demonstrating orbital fluctuation-mediated pairing and gap structures in Ba122 pnictides without phenomenological assumptions.

Findings

Orbital fluctuations induce nearly isotropic gaps on hole Fermi surfaces.

Nodal s-wave gaps appear on electron Fermi surfaces across a wide parameter range.

Impurities can convert nodal s-wave to fully gapped s++-wave state with minimal T_c reduction.

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.