Enhancement of T _c by disorder in underdoped iron pnictide superconductors

We analyze how disorder affects the transition temperature T _c of the s ^+- superconducting state in the iron pnictides. The conventional wisdom is that T _c should rapidly decrease with increasing inter-band nonmagnetic impurity scattering, but we show that this behavior holds only in the overdoped region of the phase diagram. In the underdoped regime, where superconductivity emerges from a pre-existing magnetic state, disorder gives rise to two competing effects: breaking of the Cooper pairs, which tends to reduce T _c, and suppression of the itinerant magnetic order, which tends to bring T _c up. We show that for a wide range of parameters the second effect wins; i.e., in the coexistence state T _c can increase with disorder. Our results provide an explanation for several recent experimental findings and lend additional support to s ^+- pairing in the iron pnictides.