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 [1], whereas cross-type junctions do not [2]. In addition, it has been numerical investigated that interference patterns are strongly dependent on the arrangement of the superconducting strips [3].

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 Φ_x and perpendicular magnetic field Φ_z dependence of critical currents I_c normalized by maximum critical current I_c0 in overlap-type junction. Figure 2 shows the Josephson current density distribution J_z (x,y) in the barrier layer normalized by the critical current density J_c 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.

[1] I. Rosenstein and J. T. Chen, Phys. Rev. Lett. 35, 303 (1975).
[2] S. L. Miller, K. R. Biagi, J. R. Clem, and D. K. Finnemore, Phys. Rev. B 31, 2684 (1985).
[3] R. Monaco, M. Aaroe, J. Mygind, and V. P. Koshelets, J. Appl. Phys. 104, 023906 (2008).

Fig.1: Logarithmic density plot of the critical current I_c(Φ_x,Φ_z)/I_c0 as a function of the parallel Φ_x/Φ₀ and perpendicular magnetic flux Φz/Φ₀ in overlap-type junctions.

Fig. 2: Logarithmic density plot of Josephson current density J_z(x,y)/J_c in overlap-type junctions for Φ_x/Φ₀=0 and Φ_z/Φ₀=4.

Keywords: Josephson effect, magnetic interference, overlap-type junction, cross-type junction