Renormalization group flow, competing phases, and the structure of superconducting gap in multiband models of iron-based superconductors

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 multipocket 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 angular dependence of the interactions. In a toy two-pocket model, SDW order always wins over s +/- order at perfect nesting; s +/- order only appears when doping is finite and RG flow extends long enough to overcome intrapocket Coulomb repulsion. For multipocket models, there are two new effects. First, in most cases there exists an attractive component of the interaction in s +/- channel no matter how strong intrapocket repulsion is, such that the system necessary becomes a superconductor once it overcomes the competition from the SDW state. Second, in four-pocket case (but not in five-pocket case), s +/- order wins over SDW order even for perfect nesting, if RG flow extends long enough, suggesting that SDW order is not a necessary precondition for the s +/- order. Our analytic results are in full agreement with recent numerical functional RG studies by Thomale et al. [arXiv:1002.3599 (unpublished)]