Complex state induced by impurities in multiband superconductors

Abstract

We study the role of impurities in a two-band superconductor, and elucidate the nature of the recently predicted transition from the ${s}_{\ifmmode\pm\else\textpm\fi{}}$ 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 ${s}_{\ifmmode\pm\else\textpm\fi{}}$ 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.