Effects of order parameter self-consistency in a $s_\pm$-s junction

The properties of Josephson tunneling between a single band s-wave superconductor and a two band $s_\pm$ superconductor are studied, in relation to recent experiments involving iron-based superconductors. We study a single junction and tune the order parameter (OP) phase difference across the junction. We find a variety of behaviors which are characterized by their energy-phase difference relation. The system is modeled on a lattice and treated in self-consistent mean field approximation. We also study a loop structure made with s-wave and $s_\pm$ parts with two junctions between the parts. The phase of the order parameter is then controlled by a magnetic flux threading the loop. Our analysis suggests four types of junction behaviors which are characterized by the dependence of the junction energy on the phase difference between the s-wave and the $s_\pm$ superconductors. The energy vs. phase difference curve has either one minimum at $\Delta\phi = 0,\pi$ or somewhere in between, or a double minimum structure. This leads to four different behaviors in a loop structure as a function of the flux threaded through the loop.