Nonmonotonic temperature dependence of critical current in diffusive d-wave junctions

We study the Josephson effect in D/I/DN/I/D junctions, where I, DN and D denote an insulator, a diffusive normal metal and a d-wave superconductor, respectively.The Josephson current is calculated based on the quasiclassical Green's function theory with a general boundary condition for unconventional superconducting junctions. In contrast to s-wave junctions, the product of the Josephson current and the normal state resistance is enhanced by making the interface barriers stronger. The Josephson current has a nonmonotonic temperature dependence due to the competition between the proximity effect and the midgap Andreev resonant states.