Local density of states of quasiparticles near the interface of nonuniform d-wave superconductors

The local density of states of quasiparticle (LDOS) near the interface of d-wave superconductors is investigated for various situations based on the Green's-function method of nonuniform superconductors. In the case of normal-metal-insulator-d-wave-superconductor junction, the LDOS near the interface of the superconductor strongly-depends on the angle between the normal to the interface and the crystalline axes of d-wave superconductor, on the thickness and on the height of the insulating barrier. In the case of d-wave-superconductor-insulator-d-wave-superconductor junction, bound states are formed at the interfaces of superconductors. The energy levels of bound states which include several limiting cases are explicitly obtained. The LDOS near the interface of the superconductor is strongly influenced by the bound states and it depends not only on the angle between the crystalline axes and the normal to the interface but also on the macroscopic phase difference between two superconductors.