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 $\mathrm{t}-{\mathrm{J}}_1-{\mathrm{J}}_2$ 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 quasi-degeneracy 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 $A_{1g}$ $s_{x^2{y}^2}$ channel, the nodal $A_{1g}$ $s_{x^2+y^2}$ and $B_{1g}$ $d_{x^2-y^2}$ channels are also competitive in the magnetically frustrated $J_1 \sim J_2$parameterregime\mathrm{.}An$A_{1g}+i B_{1g}$ state, which breaks time-reversal symmetry, occurs at low temperatures in part of the phase diagram. Implications for the experiments in the iron pnictides are discussed.