Self-Consistent Vertex Correction Analysis for Iron-Based Superconductors: Mechanism of Coulomb-Interaction-Driven Orbital Fluctuations

We study the mechanism of orbital/spin fluctuations due to multiorbital Coulomb interaction in iron-based superconductors, going beyond the random-phase-approximation. For this purpose, we develop a self-consistent vertex correction (SC-VC) method, and find that multiple orbital fluctuations in addition to spin fluctuations are mutually emphasized by the "multimode interference effect" described by the VC. Then, both the antiferro-orbital and ferro-orbital (=nematic) fluctuations simultaneously develop for $J/U \sim 0.1$, both of which contribute to the s-wave superconductivity. Especially, the ferro-orbital fluctuations give the orthorhombic structure transition as well as the softening of shear modulus $C_{66}$.