Low-temperature anomaly in the Josephson critical current of junctions in d-wave superconductors

We show that the Josephson critical current increases rapidly with decreasing temperature near T = 0 for tunnel junctions between anisotropic superconductors. The enhancement of the critical current has its physical origin in the midgap states bound to the tunnel barrier. The magnitude of the zero-temperature peak in a realistic junction is shown to be sensitive to the barrier transparency and barrier roughness. For some crystal orientations we find a transition from a traditional 0 junction to the unconventional pi junction with decreasing temperature.