We study the role of impurities in a two-band superconductor, and elucidate the nature of the recently predicted transition from s_{ +-} state to s_{ ++} state induced by interband impurity scattering. Using a Ginzburg-Landau theory, derived from microscopic equations, we demonstrate that close to T_c this transition is necessarily a direct one, but deeper in the superconducting state an intermediate complex state appears. This state has a distinct order parameter, which breaks the time-reversal symmetry, and is separated from the s_{ +-} and s_{ ++} states by phase transitions. Based on our results, we suggest a phase diagram for systems with weak repulsive interband pairing, and discuss its relevance to iron-based superconductors.
Categories: cond-mat.supr-con cond-mat.str-el