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

TL;DR

This study investigates how the interplay of spin and orbital fluctuations in Fe-based superconductors leads to a nodal s-wave gap structure, explaining experimental observations in BaFe₂(As,P)₂.

Contribution

It introduces a three-dimensional Hubbard model analysis showing how competing fluctuations produce a nodal s-wave gap with loop-shaped nodes.

Findings

Nodal s-wave state appears near the crossover between s++ and s± states.

Loop-shaped nodes form on electron-like Fermi surfaces.

Hole-like Fermi surfaces remain fully gapped due to orbital fluctuations.

Abstract

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 by using the random-phase-approximation. By solving the Eliashberg gap equation, we obtain the fully-gapped s-wave state with (without) sign reversal between hole-like and electron-like Fermi surfaces due to strong spin (orbital) fluctuations, so called the $s_\pm$-wave ($s_{++}$-wave) state. When both spin and orbital fluctuations strongly develop, which will be realized near the orthorhombic phase, we obtain the nodal s-wave state in the crossover region between $s_{++}$-wave and $s_\pm$-wave states. The obtained nodal s-wave state possesses the loop-shape nodes on electron-like Fermi surfaces, due to the competition between attractive and repulsive interactions in k-space. In contrast, the SC gaps on the hole-like Fermi surfaces are fully-gapped due to orbital fluctuations. The present study explains the main characters of the anisotropic gap structure in BaFe$_2$(As,P)$_2$ observed experimentally.