Critical current of an inhomogeneous Josephson junction at an intergrain boundary with a random distribution of dislocations

The critical current Jc(θ) of an intergrain boundary is calculated as a function of the contact misorientation angle θ of the granules. It is assumed that the ordering parameter is suppressed in regions near boundaries with an enhanced mechanical stress induced by randomly distributed surface dislocations. The stress distribution function is determined using a probabilistic approach. Assuming that the weak coupling at the boundary is Josephson coupling, an analytic expression is found for the angular dependence Jc(θ) (for tilt and twist boundaries). The magnitude of the residual critical current of a boundary in a strong magnetic field is estimated.