Bound states and Josephson current in mesoscopic s-wave superconductor-normal-metal-d-wave superconductor junctions

We have investigated the superconducting phase difference dependence of Andreev levels and Josephson current through a mesoscopic normal-metal layer in contact with two superconducting electrodes with s-wave and d-wave pairing symmetry ((Formula presented) junction). It is shown that, regardless of the junction length, due to the sign change of the d-wave order parameter under suitable arrangements, the zero-energy point of Andreev levels for the negative process appears at Φ=0. In particular, at zero temperature, the amplitude of the total Josephson current through the point contact (Formula presented) junction could be enhanced by the sign change of the d-wave order parameter. However, for an (Formula presented) junction of special length, the amplitude of Josephson current may be suppressed by this sign change. Moreover, as a special case, the midgap surface states discovered by Hu [Phys. Rev. Lett. 72, 1526 (1994)] are recovered naturally.