Phase Slips and Interfaces in D-Wave Superconductors

We consider a model (100) interface between two d-wave superconductors. By solving the Bogoliubov de Gennes equation on a tight binding lattice, we study the properties of the interface as a function of the interface barrier. We contrast the two scenarios: (i) an order parameter phase difference of $\theta=0$ across the interface, and (ii) a phase slip of $\theta=\pi$ across the interface. We find resonant sub-gap structure in the density of states only when there is a phase slip present. We show that the local s-wave and ``p-wave like'' order parameter components are strongly influenced by the barrier profile and by the phase slip. The temperature dependence of the local p-wave order parameter follows the underlying bulk $T_c$ for p-wave superconductivity implying that this could be measured by a suitable tunneling experiment. We also calculate the Josephson critical current as a function of the strength of the insulating barrier at the interface.