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Josephson junctions with an intrinsic phase shift of pi, so-called pi Josephson junctions, can be realized by a weak link of a <i>d</i> -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 self-consistent solutions.

Geometric $\pi$ Josephson Junction: Current-Phase Relations and Critical Current