Interplay between magnetism, superconductivity, and orbital order in a 5-pocket model for iron-based superconductors - a parquet renormalization group study

We report the results of the parquet renormalization group (RG) analysis of the phase diagram of the most general 5-pocket model for Fe-based superconductors. We use as an input the orbital structure of excitations near the five pockets made out of $d_{xz}$, $d_{yz}$, and $d_{xy}$ orbitals and argue that there are 40 different interactions between low-energy fermions in the orbital basis. All interactions flow under RG, as one progressively integrates out fermions with higher energies. We find that the low-energy behavior is amazingly simple, despite the large number of interactions. Namely, at low-energies the full 5-pocket model effectively reduces either to a 3-pocket model made of one $d_{xy}$ hole pocket and two electron pockets, or a 4-pocket model made of two $d_{xz}/d_{yz}$ hole pockets and two electron pockets. The leading instability in the effective 4-pocket model is a spontaneous orbital (nematic) order, followed by $s^{+-}$ superconductivity. In the effective 3-pocket model orbital fluctuations are weaker, and the system develops either $s^{+-}$ superconductivity or stripe SDW. In the latter case, nematicity is induced by composite spin fluctuations.