Effect of weak disorder on the phase competition in iron pnictides

We analyze the effect of weak disorder on the competition between antiferromagnetic order and superconductivity in a model for iron-based superconductors. Under the assumption of an approximate particle-hole symmetry we show that conventional $s^{++}$ superconductivity cannot be realized in the case of coexisting magnetic and superconductive orders, observed experimentally at intermediate doping levels. This result holds for arbitrary impurity concentrations, and, in particular, in the clean limit. The inclusion of disorder further amplifies the phase competition between itinerant antiferromagnetism and conventional superconductivity. In addition, we analyze the effect of disorder on the characteristic length scales of the two order parameters, and find that in a disordered sample the staggered moment fluctuates on shorter scales than the superconductive order parameter.