Renormalization group flow, competing phases, and the structure of superconducting gap in multi-band models of Iron based superconductors

TL;DR

This paper uses analytical renormalization group analysis on multi-band models of iron-based superconductors to explore the competition between magnetic and superconducting orders, revealing conditions favoring superconductivity even at perfect nesting.

Contribution

It extends previous toy models by analyzing more realistic multi-pocket models with angular dependence, discovering new conditions where superconductivity can dominate.

Findings

In multi-pocket models, an attractive s+- interaction component always emerges.

Superconductivity can prevail over SDW order even at perfect nesting in 3-pocket models.

Results align with recent numerical RG studies, confirming the robustness of the findings.

Abstract

We perform an analytical renormalization group (RG) study to address the role of Coulomb repulsion, the competition between extended s-wave superconducting order (s+-) and the spin-density wave (SDW) order and the angular dependence of the superconducting gap in multi-pocket models of Iron based superconductors. Previous analytic RG studies considered a toy model of one hole and one electron pocket. We consider more realistic models of two electron pockets and either two or three hole pockets, and also incorporate the angular dependence of interaction. We neglect for simplicity one of the two hole pockets centered at k=0, which is less nested with electron pockets, i.e., consider 3-pocket and 4-pocket models. In a toy 2-pocket model, SDW order always wins over s+- order at perfect nesting, and s+- order only appears at a finite doping, and only if RG flow extends long enough to overcome intra-pocket Coulomb repulsion. For multi-pocket models, we find two new effects. First, there always exists an attractive component of the interaction in s+- channel, such that the system necessary becomes a superconductor once it overcomes the competition from the SDW state. Second, in 3-pocket case (but not in 4-pocket case), there are situations when s+- order wins over SDW order even for perfect nesting, suggesting that SDW order is not a necessary pre-condition for the s+- order. Our results are in good agreement with recent numerical functional RG studies by Thomale et al. [arXiv:1002.3599]