Effects of grain-boundaries in superconducting materials

We examine the effects of grain-boundaries on the order-parameter and critical-currents in superconductors. We use a geometrical model of the lattice structure of grain-boundaries. We solve the Bogoliubov-de Gennes equation using the Recursion Method to obtain the self-consistent BCS gap function Delta and the local density of states N(E) near the boundary. Imposing a phase difference across the boundary we calculate the supercurrent and hence obtain the critical-current, I-c, of the junction.