Superconductivity in two-leg ladder iron selenides

Recently, evidence of superconductivity has been discovered in the single-layer potassium-doped iron selenide that consists of weakly coupled two-leg iron ladders (Wei Li {\it et al.}, arXiv:1210.4619). Using a self-consistent mean-field approximation, we analyze the pairing symmetry and structure of the multi-orbital $t$-$J$ model defined in these two-leg ladder systems. Similar to the case of the iron pnictides, a modified $s$-wave pairing state is stabilized by the next-nearest-neighbor superexchange $J_2$. The presence of competing states will be discussed. Our result demonstrates the potential importance of the local magnetic couplings in iron-based superconductors.