Iron pncitide superconductors studied by the functional renormalization group

We review the functional renormalization group (fRG) approach to the superconducting iron pnictides. We start with simple two-pocket models for the basic weak-coupling picture and then build up the complexity of the many-orbital problem in two steps. In this way we discuss what one can learn about the phase diagrams, superconducting pairing mechanism and competing orders in iron arsenides. Special attention is devoted to where this theoretical approach exposes similarities and differences between the physics of the pnictides and that of the high-T _c cuprates. Finally, we describe some challenges for getting a consistent theoretical understanding of the new iron superconductor material class in a combination of ab-initio and functional renormalization group approaches.