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We report the results of a parquet renormalization group (RG) study ofcompeting instabilities in the full 2D four pocket, three orbital low-energymodel for iron-based superconductors. We derive and analyze the RG flow of thecouplings, which describe all symmetry-allowed interactions between low-energyfermions. Despite that the number of the couplings is large, we argue thatthere are only two stable fixed trajectories of the RG flow and one weaklyunstable fixed trajectory with a single unstable direction. Each fixedtrajectory has a finite basin of attraction in the space of initial systemparameters. On the stable trajectories, either interactions involving only$d_{xz}$ and $d_{yz}$ or only $d_{xy}$ orbital components on the electronpockets dominate, while on the weakly unstable trajectory interactionsinvolving $d_{xz}$ ($d_{yz}$) and $d_{xy}$ orbital states on the electronpockets remain comparable. The behavior along the two stable fixed trajectorieshas been analyzed earlier [A.V. Chubukov, M. Khodas, and R.M. Fernandes,arXiv:1602.05503]. Here we focus on the system behavior along the weaklyunstable trajectory and apply the results to FeSe. We find, based on theanalysis of susceptibilities along this trajectory, that the leadinginstability upon lowering the temperature is towards a {\it three-component}d-wave orbital nematic order. Two components are the differences betweenfermionic densities on $d_{xz}$ and $d_{yz}$ orbitals on hole pockets and onelectron pockets, and the third one is the difference between the densities of$d_{xy}$ orbitals on the two electron pockets. We argue that this order isconsistent with the splitting of band degeneracies, observed in recentphotoemission data on FeSe by A. Fedorov et al [arXiv:1606.03022].

physical review. b./physical review. b

Competing instabilities, orbital ordering and splitting of band  degeneracies from a parquet renormalization group analysis of a 4-pocket  model for iron-based superconductors: application to FeSe