Theory of the interplay between the superconductivity and the blocked antiferromagnetic order in AyFe2-xSe2

Based on an effective two-orbital tight-binding model, we examine the possible superconducting states in iron-vacancy-ordered AyFe2-xSe2. In the presence of ordered vacancies and blocked antiferromagnetic order, it is shown that the emergent SC pairing is the nodeless next-nearest-neighbor (NNN)-pairing due to the dominant antiferromagnetic (AFM) interaction between the inter-block NNN sites. In particular, we show that due to the ordered vacancies and the associated blocked AFM order, the interplay between the superconducting and AFM states results in three distinct states in the phase diagram as doping is varied. The divergent experimental observations can be accounted for by considering the different charge carrier concentrations in their respective compounds.