Quasiparticle interface states in junctions involving d-wave superconductors

The influence of surface pair breaking, barrier transmission, and phase difference on quasiparticle bound states in junctions with d-wave superconductors is examined. Based on the quasiclassical theory of superconductivity, an approach is developed to handle interface bound states. It is shown in superconductor-insulator-superconductor junctions that low-energy bound states get their energies reduced by surface pair breaking, which can be taken into account by introducing an effective order parameter for each superconductor at the junction barrier. More interestingly, for the interface bound states near the continuous spectrum the effect of surface pair breaking may result in a splitting of the bound states. In the tunneling limit this can lead to a square-root dependence of a nonequilibrium Josephson current on the barrier transmission, which means an enhancement as compared to the conventional critical current linear in the transmission. Reduced broadening of bound states in normal-metal-insulator-superconductor junctions due to surface pair breaking is found.