Properties of the zero energy Andreev bound state in a two sublattice SNS junction

We study properties of the zero energy Andreev bound state in a superconductor-normal metal-superconductor(SNS) junction consisting of two intrinsic degrees of freedom. The superconductors on either sides of the normal metal are assumed to have two sublattices with an $intra$-sublattice pairing with a phase of zero or $\pi$ between the two sublattices. In addition, we add a uniform $inter$-sublattice pairing and study its effect on the local density of states (LDOS). In particular, we find that as the inter-sublattice pairing is turned on, the zero bias peak (ZBP) is unstable (robust) when the phase difference across the sublattices is $\pi$ (zero). We discuss the relevance of our results to the recently proposed odd parity $-\eta$ pairing ground states in Iron based superconductors (FeSCs).