Orbital order from the on-site orbital attraction

We study the model of Fe-based superconductors with intraorbital attraction, designed to favor a spontaneous orbital polarization. Previous studies of this model within the two-orbital approximation indicated that the leading instability is toward s-wave superconductivity and the subleading one is toward anti-ferro-orbital order, which breaks the translational symmetry of the crystal. The two-orbital approximation is, however, not consistent with the Fermi surface geometry of Fe superconductors, as it yields the wrong position of one of the hole pockets. Here we analyze the model with the same interaction but with realistic Fermi surface geometry (two hole pockets at the center of the Brillouin zone and two electron pockets at its boundary). We apply the parquet renormalization-group (pRG) technique to detect the leading instability upon the lowering of the temperature. We argue that the pRG analysis strongly favors a q=0 orbital order, which in the band basis is a d-wave Pomeranchuk order.