Near-degeneracy of several pairing channels in multiorbital models for the Fe pnictides

Weak-coupling approaches to the pairing problem in the iron pnictide superconductors have predicted a wide variety of superconducting ground states. We argue here that this is due both to the inadequacy of certain approximations to the effective low-energy band structure, and to the natural near degeneracy of different pairing channels in superconductors with many distinct Fermi surface sheets. In particular, we review attempts to construct two-orbital effective band models, the argument for their fundamental inconsistency with the symmetry of these materials, and compare the dynamical susceptibilities of two- and five-orbital tight-binding models. We then present results for the magnetic properties, pairing interactions and pairing instabilities within a five-orbital tight-binding random phase approximation model. We discuss the robustness of these results for different dopings, interaction strengths and variations in band structures. Within the parameter space explored, an anisotropic, sign-changing s-wave (A1g) state and a (B1g) state are nearly degenerate, due to the near nesting of Fermi surface sheets.