Origin of the variety of superconducting gap structure in iron-based superconductors: competition between orbital and spin fluctuations

To understand the pairing mechanism in iron-based superconductors, we study the three-dimensional gap structure based on the orbital fluctuation theory. We focus on the fully-gapped state in (i) heavily electron-doped KFe$_2$Se$_2$ [1], nodal gap structure in (ii) isovalent-doped BaFe$_2$(As,P)$_2$, and strongly band-dependent gap structure in (iii) hole-doped (Ba,K)Fe$_2$As$_2$. Based on the three-dimensional ten orbital model for (i), we obtain orbital-fluctuation-mediated fully-gapped $s_{++}$ wave state without sign reversal. For (ii), we reproduce the loop-shaped nodal structure on the electron-Fermi surface, due to the competition between orbital and spin fluctuations. For (iii), we obtain a drastic change in the gap structure by hole-doping, reflecting the variation of orbital fluctuations due to the topological change of electron-pockets. These results indicate the significant role of orbital fluctuations in iron-based superconductors. [1] Saito et al., PRB 83, 140512(R) (2011)