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 BaFe2(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.