Josephson junctions with an intrinsic phase shift of pi, so-called pi Josephson junctions, can be realized by a weak link of a d-wave superconductor with an appropriate boundary geometry. A model for the pairing potential of an according weak link is
introduced which allows for the calculation of the influence of geometric parameters and temperature. From this model, current-phase relations and the critical current of the device are derived. The range of validity of the model is determined by comparison with selfconsistent solutions.
We show that a constriction-type Josephson junction realized by an epitactic thin film of a d-wave superconductor with an appropriate boundary geometry exhibits intrinsic phase differences between 0 and pi depending on geometric parameters and temper
ature. Based on microscopic Eilenberger theory, we provide a general derivation of the relation between the change of the free energy of the junction and the current-phase relation. From the change of the free energy, we calculate phase diagrams and discuss transitions driven by geometric parameters and temperature.
A novel way to realize a pi Josephson junction is proposed, based on a weak link in an unconventional d-wave superconductor with appropriately chosen boundary geometry. The critical current of such a junction is calculated from a fully selfconsistent
solution of microscopic Eilenberger theory of superconductivity. The results clearly show, that a transition to a pi Josephson junction occurs for both low temperatures and small sizes of the geometry.
