Antiferromagnetic Josephson junction: Nonreciprocity and sublattice selective transport of Cooper triplets

The Josephson junction under consideration is composed of two s-wave superconducting contacts deposited on the top of a two-dimensional antiferromagnet (AF). Triplet Cooper correlations in AF are provided by thin ferromagnetic spacers between AF and superconducting contacts. The problem is considered in the regime of a weak tunneling of electrons between these contacts and AF. The transport of electron Cooper's pairs under the stationary phase bias in the disordered AF is treated within the formalism of equilibrium Green's functions and the Born approximation for electrons which are scattered by nonmagnetic impurities. The system of diffusion equations is derived for three triplet components of Cooper-correlated electron pairs. These spin projections are coupled to each other due to interplay of the spin-orbit interaction and AF order. Moreover, the diffusion equations are sublattice-dependent. It is shown that such a staggered behavior will lead to the nonreciprocal Josephson current, if the tunneling of electrons between contacts and AF is different for different sublattices.