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 equal to zero or π 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 π (zero). We discuss the relevance of our results to the recently proposed odd-parity η pairing ground states in iron-based superconductors (FeSCs).