d-wave pairing near the boundary of superconductors

On the basis of the tight-binding model defined on a square lattice with a straight boundary in the y direction, we investigate the boundary effect in d-wave superconductors. The Bogoliubov-de Gennes equation describing the quasiparticles are self-consistently solved at a number of temperatures. The present calculation shows that there is an oscillatory behavior appearing in the pairing parameter near the boundary. The length scale of such an inhomogeneity is about 10 lattice constants. At the boundary, the y-direction pairing is considerably depressed, while the x-direction pairing is enhanced. We also study the surface effect in the alpha-axis Josephson tunneling between high-T-c superconductors. The temperature dependence of the Josephson critical current is investigated through numerical calculations. It is shown that the present theory is in very good agreement with experiments.