Maximum limit of connectivity in rectangular superconducting films with an oblique weak link
A method for measuring the electrical connectivity between parts of a rectangular superconductor was developed for weak links making an arbitrary angle with the long side of the sample. The method is based on magneto-optical observation of characteristic lines where the critical current makes discontinuous deviations in the flow direction to adapt to the non-uniform condition created by the presence of the weak link. Assuming the Bean critical state model in the full penetration regime for a sample submitted to a perpendicular magnetic field, the complete flow pattern of screening currents is reconstructed, from which the transparency of the weak link, i.e., the ratio between its critical current and that of the pristine sample, $\tau = \frac{J_i}{J_c}$, is then related to the angle $\theta$ formed by two characteristic discontinuity lines which, in turn, are intimately associated to the presence of the weak link. The streamline distribution is compared with magneto-optical observations of the flux penetration in Nb superconducting films, where a weak link was created using focused ion beam milling. The present work generalizes previous analyses in which the weak link was perpendicular to the long sides of the rectangular sample. Equations and measurements demonstrate that the relationship between the transparency and the angle $\theta$ is not affected by the tilting of the weak link. Noticeably, in order to attain optimum connectivity, the weak link critical current can be less than that of the pristine sample, namely, $\tau _{max}=\sin \Phi$, where $\Phi$ is the tilt angle of the weak link. This expression generalizes the previous result of $\tau _{max}=1$ for $\Phi=$ 90$^\circ$.