Pinhole junctions in d-wave superconductors

We present a self consistent treatment of pinhole junctions in $d_{x^2-y^2}$ superconductors. The current-phase relation $j_s(\chi)$ is studied at different temperatures and at different angles $\alpha$ between the crystal $\hat a$-axis and the junction (surface) normal. We show that the critical current of a junction can be reduced by pair-breaking effects at the separation. We also study the Josephson energy of a pinhole as a function of the phase difference across the junction. In particular are mapped the positions of the energy minima $\chi_{min}$ at different temperatures as functions of ($\alpha_L,\alpha_R$), the crystal orientations of the left and right superconductors. With decreasing temperature there is an increasing range of crystal orientations where $\chi_{min}$ varies continuously from 0 to $\pi$.