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Anomalous magnetic interference of cross-type Josephson junctions exposed to oblique magnetic fields

Gauge-invariant phase difference and critical currents of cross-type Josephson junctions with thin and narrow superconducting strips exposed to three-dimensional magnetic fields are theoretically investigated. When a sandwich-type Josephson junction in the xy plane is exposed to parallel magnetic fields Hx and Hy, the phase difference linearly depends on the spatial coordinates, x and y, and the critical currents exhibit the standard Fraunhofer-type magnetic interference. The perpendicular field Hz, on the other hand, nonlinearly modulates the distribution of the phase difference and the critical currents as the functions of the oblique field exhibit anomalous magnetic interference. We obtain simple analytical expressions for critical currents of small cross-type junctions by neglecting the effects of self-field and trapped vortices. The resulting dc critical currents show anomalous and diverse interference patterns depending on the parallel and perpendicular magnetic fields