The effect of magnetic order on the superconducting gap in the co-existence phase of Fe-pnictides

We study the structure and symmetry of the superconducting gap in the presence of spin density wave (SDW) order in iron-based superconductors. We show that SDW order generally induces a spin-triplet component of the gap, in addition to the conventional spin singlet. We further show that, in some range of temperatures below $T_c$, the phases of superconducting order parameters on different reconstructed Fermi surfaces differ by an amount other than 0 or $\pi$, i.e., superconductivity directly reflects the breaking of time-reversal symmetry by SDW order. We specifically consider co-existing SDW and superconducting orders in a model with circular hole pockets and elliptic electronic pockets and present analytical results for the phase diagram and the structure of the superconducting gap at various temperatures.