he gauge-invariant phase difference in a Josephson junction is modulated by the magnetic field and the magnetic field dependence of the DC critical current shows a Fraunhofer-like interference pattern. Magnetic interference is an important phenomenon in applications of superconducting quantum interference devices. It has been reported that the overlap-type junctions show magnetic interference of critical currents under perpendicular magnetic fields , whereas cross-type junctions do not . In addition, it has been numerical investigated that interference patterns are strongly dependent on the arrangement of the superconducting strips .
In this study, we analytically show the magnetic interference of critical currents and Josephson current density through the barrier layer in cross-type and overlap-type junctions under applying oblique magnetic fields. We assume that the self-field and the magnetic screening is sufficiently small. Figure 1 shows the parallel Φx and perpendicular magnetic field Φz dependence of critical currents Ic normalized by maximum critical current Ic0 in overlap-type junction. Figure 2 shows the Josephson current density distribution Jz (x,y) in the barrier layer normalized by the critical current density Jc in overlap-type junction. By comparing these results for cross-type and overlap-type junctions, we consider how the strips arrangements and the junction geomety affect the magnetic interference of critical currents.
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Fig.1: Logarithmic density plot of the critical current Ic(Φx,Φz)/Ic0 as a function of the parallel Φx/Φ0 and perpendicular magnetic flux Φz/Φ0 in overlap-type junctions.
Fig. 2: Logarithmic density plot of Josephson current density Jz(x,y)/Jc in overlap-type junctions for Φx/Φ0=0 and Φz/Φ0=4.
Keywords: Josephson effect, magnetic interference, overlap-type junction, cross-type junction