Two-dimensional magnetic field dependence of zero and finite voltage steps in current-voltage characteristics of rectangular shape niobium tunnel junctions

Graphical abstractDisplay Omitted Highlights? Josephson current Ic through Nb superconducting junction was measured. ? Ic dependence on Hx, Hy magnetic fields was product of Fraunhofer pattern. ? Numerical simulation of Ic-(Hx, Hy) matched the measured result. ? Modulation period inversely proportional to the vertical edge length of junction. ? Resonant current steps studied by superconducting planar circuit model. Modulation characteristics of Josephson current through rectangular shape niobium/aluminum-oxide/niobium superconducting junctions have been studied by two-dimensional (2-D) scanning of the external magnetic field. In order to obtain the magnetic field dependence automatically, two pairs of Helmholtz coils are driven by two current sources with GPIB (General Purpose Interface Bus) system. The 2-D magnetic field dependences of the Josephson current and the resonant current steps of the current-voltage characteristics of the Nb/Al-oxide/Nb tunnel junction have been measured. The Ic-(Hx-Hy) characteristics are the product of two Fraunhofer diffraction patterns in Hx and Hy directions parallel to each junction edge, and are also numerically calculated by assuming that distribution of phase difference γ and the junction current density I0 inside the rectangular shape junction area have been modulated in perpendicular direction to the external magnetic field. This modulation period is inversely proportional to the junction length perpendicular to the external magnetic field. The resonant current steps are also considered using superconducting planar circuit model. The distributions of the magnetic flux, the electrode current and the junction current have been studied.