Functional renormalization-group study of the doping dependence of pairing symmetry in the iron pnictide superconductors

We use the functional renormalization group to analyze the phase diagram of a four-band model for the iron pnictides subject to band interactions with certain A1g momentum dependence. We determine the parameter regimes where an extended s -wave pairing instability with and without nodes emerges. For electron doping, the parameter regime in which a nodal gap appears is in correspondence to recent predictions, however, at very low Tc. Upon hole doping, the s -wave gap never becomes nodal: above a critical strength of the intraband repulsion, the system favors an exotic extended d -wave instability on the enlarged hole pockets. At half filling, we find that a strong momentum dependence of interband pair hopping yields an extended s -wave instability instead of spin-density wave ordering. These results demonstrate that an interaction anisotropy around the Fermi surfaces generally leads to a pronounced sensitivity of the pairing state on the system parameters.