Disorder induced transition between $s_{\pm}$ and $s_{++}$ states Fe-based superconductors*

The symmetry and structure of the superconducting gap in recently discovered Fe-based materials is one of the main challenges in this exciting new field (see, e.g. P.J. Hirschfeld, M.M. Korshunov, and I.I. Mazin, Rep. Progr. Phys. 2011). We have reexamined the problem of disorder in 2-band superconductors, and shown within the framework of the $T$-matrix approximation that the suppression of $T_c$ can be described by a single parameter depending on the intra- and interband impurity scattering rates. $T_c$ is shown to be more robust against nonmagnetic impurities than would be predicted in the trivial extension of Abrikosov-Gor'kov theory. We find disorder-induced transition from the $s_{\pm}$ state to a gapless and then to a fully gapped $s_{++}$ state, controlled by the sign of the average coupling constant.