Local single-particle tunneling characteristics between two d-wave superconductors each containing midgap states at a grain boundary

We have calculated the local single-particle tunneling characteristics between two points each at the vicinity of a grain boundary of a d-wave superconductor. Conductance peak features appear at zero energy, Delta (0), and 2 Delta (0), where Delta (0) is the maximum gap, due to midgap states (MS's) to MS's, MS's to gap-edge, and gap-edge to gap-edge tunneling, respectively. Negative conductance also appears just outside the zero-energy peak (at low T's).