Matrix-pairing states in the alkaline Fe-selenide superconductors: exotic Josephson junctions

Multi-band alkaline Fe-selenides and the heavy-fermion CeCu₂Si₂ show signatures of fully-gapped but sign-changing superconductivity. A two-orbital pairing state, called sτ₃, with non-trivial matrix structure, was proposed to reconcile the seemingly contradictory properties of these superconductors. Motivated by the orbital-selective pairing structure, we study prototypical Josephson junctions where at least one of the leads is in a superconducting state of this kind. The limit of two degenerate orbitals reveals two remarkable properties. One is the emergence of gapless bound states which are purely electron- and hole-like in the N part, and which persist under arbitrary global phase differences for sτ₃-N-sτ₃ junctions. The other is the absence of static Josephson currents when both leads are superconducting. In these aspects, sτ₃ junctions are significantly different from conventional Josephson junctions. We find that the gapless bound states are protected by an orbital-exchange symmetry, although the protection is not topological. Junctions which break this symmetry, such as sτ₃-N-s, have gapped Andreev bound states. The Josephson effect re-emerges once the degeneracy of the two orbitals is lifted. Our results indicate that junctions involving sτ₃ pairing in alkaline Fe-selenides will generically have bound states with a small gap and a greatly suppressed Josephson current.