Influences of broken time-reversal symmetry on the dc Josephson effects in d-wave superconductors

In order to examine the influences of the spatial dependence of the pair potential on the Josephson current, the de Josephson current in d-wave superconductors is calculated using self-consistently determined pal potentials. The results show that the suppression of the d-wave pair potential near the insulator does not have a serious effect on the properties of the Josephson current. On the other hand, drastic changes are obtained due to the inducement of a subdominant a-wave component, which spontaneously breaks time-reversal symmetry. In particular, a rapid enhancement of the Josephson current at low temperature predicted in previous formulas is strongly suppressed.