Theory of fully-gapped s++ wave states in BaFe2(As,P)2 and LiFeAs: Analysis beyond the Migdal-Eliashberg formalism

Both the spin fluctuation mediated S+- wave state and the orbital fluctuation mediated S++ wave state have been studied in various Fe-based superconductors. In BaFe2(As,P)2, the spin fluctuation theory predicts that the horizontal node appears on the hole like Fermi surface composed of z2 orbital [1]. In contrast, fully-gapped s++ wave state is obtained based on the orbital fluctuation theory [2], by introducing the phenomenological quadrupole interaction. To confirm the validity of this phenomenological approach, we analyze the two-dimensional Hubbard model for BaFe2(As,P)2, by focusing on the vertex corrections dropped in conventional Migdal-Eliashberg gap equation. We find that strong inter-orbital attractive pairing interaction among z2, xz, yz, xy orbitals is caused by the orbital fluctuations, due to the quadrupole interaction given by the Aslamazov-Larkin vertex correction. Therefore, the fully-gapped s++ wave state is naturally obtained, consistently with Ref. [2]. In addition, we apply the same method to LiFeAs, and succeed in reproducing the experimental gap structure in terms of the orbital fluctuation mechanism. [1] K. Suzuki et al, JPSJ 80,013710 (2011). [2] T. Saito et al, PRB 88, 045115 (2013)