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Phase diagram of Josephson junction between s and s+- superconductors in dirty limit

The s+- state in which order parameter has different signs in different bands is a leading candidate for the superconducting state in the iron based superconductors. We investigate a Josephson junction between s and s+- superconductors within microscopic theory. Frustration, caused by interaction of the s-wave gap parameter with the opposite-sign gaps of the s+- superconductor, leads to nontrivial phase diagram. When the partial Josephson coupling energy between the s-wave superconductor and one of the s+- bands dominates, s-wave gap parameter aligns with the order parameter in this band. In this case the partial Josephson energies have different signs corresponding to signs of the gap parameters. In the case of strong frustration, corresponding to almost complete compensation of the total Josephson energy, a nontrivial time-reversal-symmetry breaking (TRSB) state realizes. In this state all gap parameters become essentially complex. As a consequence, this state provides realization for so-called ϕ-junction with finite phase difference in the ground state. The width of the TRSB state region is determined by the second harmonic in Josephson current, ~ sin(2ϕ), which appears in the second order with respect to the boundary transparency. Using the microscopic theory, we establish range of parameters where different states are realized. Our analysis shows insufficiency of the simple phenomenological approach for treatment of this problem.