ac Josephson effect in superconducting d-wave junctions

We study theoretically the ac Josephson effect in superconducting planar d- wave junctions. The insulating barrier assumed to be present between the tw o superconductors may have arbitrary strength. Many properties of this syst em depend on the orientation of the d-wave superconductor: we calculate the ac components of the Josephson current. In some arrangements there is subs tantial negative differential conductance due to the presence of midgap sta tes. We study how robust these features are to finite temperature and also comment on how the calculated current-voltage curves compare with experimen ts. For some other configurations (for small barrier strength) we find zero -bias conductance peaks due to multiple Andreev reflections through midgap states. Moreover, the odd ac components are strongly suppressed and even ab sent in some arrangements. This absence will lead to a doubling of the Jose phson frequency. All these features are due to the d-wave order parameter c hanging sign when rotated 90 degrees. Recently, there have been several the oretical reports on parallel current in the d-wave case for both the statio nary Josephson junction and for the normal-metal-superconductor junction. A lso in our case there may appear current density parallel to the junction, and we present a few examples when this takes place. Finally, we give a fai rly complete account of the method used and also discuss how numerical calc ulations should be per-formed in order to produce current-voltage curves.