π-vortex state in a long 0-π Josephson junction

We study the static configurations of a one-dimensional 0-π Josephson junction, consisting of an s-d junction or selected boundaries between three suitably oriented d-wave superconductors. We find that a d-wave-type interference pattern can only be observed in the field-modulated critical current if the junction is short compared to the Josephson penetration depth. However, the behavior of a 0-π junction is found to be indistinguishable from that of a 0 junction between s-wave superconductors in the long junction limit, due to the formation of a π vortex.