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 two superconductors may have arbitrary strength. Many properties of this system depend on the orientation of the d-wave superconductor: we calculate the ac components of the Josephson current. In some arrangements there is substantial negative differential conductance due to the presence of midgap states. We study how robust these features are to finite temperature and also comment on how the calculated current-voltage curves compare with experiments. 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 absent in some arrangements. This absence will lead to a doubling of the Josephson frequency. All these features are due to the d-wave order parameter changing sign when rotated 90 degrees. Recently, there have been several theoretical reports on parallel current in the d-wave case for both the stationary Josephson junction and for the normal-metal-superconductor junction. Also 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 fairly complete account of the method used and also discuss how numerical calculations should be per-formed in order to produce current-voltage curves.