Nodal gap structure in Fe-based superconductors due to the competition between orbital and spin fluctuations

To understand the origin of the nodal gap structure realized in BaFe ₂(As,P)₂, we study the three-dimensional gap structure based on the three-dimensional ten-orbital Hubbard model with quadrupole interaction. In this model, strong spin and orbital fluctuations develop when the random-phase approximation is used. By solving the Eliashberg gap equation, we obtain the fully gapped s-wave state with (without) sign reversal between holelike and electronlike Fermi surfaces due to strong spin (orbital) fluctuations, the so-called s_±-wave (s₊₊-wave) state. When both spin and orbital fluctuations develop strongly, which will be realized near the orthorhombic phase, we obtain a nodal s-wave state in the crossover region between the s₊₊-wave and s_±-wave states. The nodal s-wave state obtained possesses loop-shaped nodes on electronlike Fermi surfaces, due to the competition between attractive and repulsive interactions in k space. In contrast, the superconducting gaps on the holelike Fermi surfaces are fully gapped due to orbital fluctuations. The present study explains the main characteristics of the anisotropic gap structure in BaFe₂(As,P)₂ observed experimentally.