On the effect of Van Hove singularities on the critical current of high-T_c junctions

We show that the Josephson critical current between two 2-dimensional superconductors can be strongly affected by the Van Hove singularity of the density of states characteristic of 2-dimensional metals. In particular, when the Fermi level falls at the singularity, the critical current is zero for certain crystallographic misorientations between the two superconductors. This effect sems to have been observed recently in high-T_c grain boundary junction experiments.