Superconductivity in multi-orbital t-J₁-J₂ model and its implications for iron pnictides

Motivated by the bad metal behavior of the iron pnictides, we study a multi-orbital t-J₁-J₂ model and investigate possible singlet superconducting pairings. Magnetic frustration by itself leads to a large degeneracy in the pairing states. The kinetic energy breaks this into a quasidegeneracy among a reduced set of pairing states. For small electron and hole Fermi pockets, an A_1g state dominates over the phase diagram but a B_1g state has close-by energy. In addition to the nodeless A _1g s_x2_y2 channel, the nodal A_1g s_x2+_y2 and B_1g d_x2-_y2 channels are also competitive in the magnetically frustrated J₁ ∼ J₂ parameter regime. An A_1g +iB_1g state, which breaks timereversal symmetry, occurs at low temperatures in part of the phase diagram. Implications for the experiments in the iron pnictides are discussed.