Effects of competing Neel-type magnetic fluctuations and nematic order on the superconductivity of the iron arsenides*

In many iron-based superconductors, the presence of two matching electron pockets displaced by $(\pi,\pi)$ gives rise to Neel-type magnetic fluctuations, in addition to the usual stripe-type magnetic fluctuations peaked at $(\pi,0)$ and $(0,\pi)$. Indeed, recent neutron scattering experiments observed both types of fluctuations in certain hole-doped iron pnictides, which intriguingly do not display superconductivity. In this talk, we employ an Eliashberg approach to address the impact of competing $(\pi,\pi)$ and $(\pi,0)$ fluctuations on the superconducting state of the iron arsenides. We show that, surprisingly, even weak short-ranged Neel fluctuations strongly suppress the $s^{\pm}$ state. The main contribution to this suppression comes from a repulsive $s^{\pm}$ interaction induced by the Neel fluctuations, and not from the inelastic scattering pair-breaking that they promote. Upon enhancing the strength of the Neel fluctuations, a d-wave state appears, preceded by either an intermediate $s+id$ state or a non-superconducting region, forming a two-dome structure. We compare our results to experimental findings, and discuss their implications to the optimal $T_c$ of the iron arsenides, arguing that it can be enhanced via a tetragonal-symmetry breaking induced by nematic order.