Superconductivity in the multiband matrix t-J1-J2 model and its implications for the iron pnictides

We describe the iron pnictides in terms of an incipient Mott picture. We use local moments with frustrating J1-J2 interactions to model the incoherent electronic excitations, and couple them to the coherent electronic carriers. The resulting multiband matrix t-J1-J2 model is analyzed in terms of a slave boson theory, leading to a superconducting phase diagram as a function of doping and J2/J1 ratio. The different pairing symmetries reflect a competition between the strong coupling effects of the J1-J2 interactions, and the kinematic effects associated with the multiple sheets of Fermi surfaces.