We study the role of impurities in a two-band superconductor, and elucidate the nature of the recently predicted transition from the $s_{\pm }$ state to the $s_{++}$ 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 $s_{\pm }$ and $s_{++}$ states by continuous 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.

• Received 25 June 2013
• Revised 21 February 2014

DOI:https://doi.org/10.1103/PhysRevB.89.100505