Doping-dependent pairing symmetry in the Iron-Pnictides

We use the functional renormalization group method to analyze the phase diagram of a 4-band model for the iron-pnictides subject to band interactions with certain A_{1g} momentum dependence. We determine the parameter regimes where an extended s-wave pairing instability with and without nodes emerges. On the electron-doped side, the parameter regime in which a nodal gap appears is found to be much narrower than recently predicted in arXiv:0903.5547. On the hole-doped side, the extended s-wave pairing never becomes nodal: above a critical strength of the intra-band repulsion, the system favors an exotic extended d-wave instability on the enlarged hole pockets at much lower T_c. At half filling, we find that a strong momentum dependence of inter-band pair hopping yields an extended s-wave instability instead of spin-density wave (SDW) 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.