Anomalous proximity effects at the interface of s and s+- superconductors

We study proximity effects close to a boundary between s and s+- superconductors. Frustration, caused by interaction of the s-wave gap parameter with the opposite-sign gaps of s+- superconductor, leads to several anomalous features. In the case of strong frustration a nontrivial time-reversal-symmetry breaking (TRSB) state, with nonzero phase angles between all gap parameters, is possible. In a more typical state, the s-wave order parameter is aligned with one of the s+- gaps. The other (anti-aligned) gap induces negative feature in the s-wave density of states, which can serve as a fingerprint of s+- state. Another consequence of the frustration is an extended region in the parameter space in which s-wave superconductivity is suppressed, despite being in contact with nominally stronger superconductor. This negative proximity effect is always present for the TRSB state, but extends even into the aligned states. We study these effects within a simple microscopic model assuming dirty limit in all bands, which allows us to model the system in terms of minimum number of the most relevant parameters. The described anomalous features provide a route to establishing the possible s+- state in the iron-based superconductors