Renormalization group flow, competing phases, and the structure of superconducting gap in multi-band 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 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]Comment: 24 pp, 25 figures, published in PRB, uploading published versio

Superconductivity from repulsive interaction

The BCS theory of superconductivity named electron-phonon interaction as a glue that overcomes Coulomb repulsion and binds fermions into pairs which then condense and superconduct. We review recent and not so recent works aiming to understand whether a nominally repulsive Coulomb interaction can by itself give rise to a superconductivity. We first discuss a generic scenario of the pairing by electron-electron interaction, put forward by Kohn and Luttinger back in 1965, and then turn to modern studies of the electronic mechanism of superconductivity in the lattice models for the cuprates, the Fe-pnictides, and the doped graphene. We show that the pairing in all three classes of materials can be viewed as lattice version of Kohn-Luttinger physics, despite that the pairing symmetries are different. We discuss under what conditions the pairing occurs and rationalize the need to do parquet renormalization-group analysis. We also discuss the interplay between superconductivity and density-instabilities.Comment: 71 pages, To be published in "Proceedings of the XVII Training Course in the physics of Strongly Correlated Systems", Vietri sul Mare (Salerno), Italy. New references added, Typos correcte