Hexagonal symmetry of magnetic field dependence of Josephson current through triangle shape superconducting junctions

We have found hexagonal symmetry in the dependence of Josephson current of triangle shape junctions upon external magnetic field. Niobium/aluminum-oxide/niobium junctions are fabricated using magnetron sputtering of niobium and thermal oxidation of aluminum layers. Selective niobium anodization process has been used to define junction areas. In the case of square shaped junction, dependence of Josephson current obtained by two dimensional scanning of the external field parallel to aluminium-oxide layer, have become the product of the two Fraunhofer patterns in the direction Hx, Hy parallel to each edge of this square junction area (1). Sub peaks have been observed in four directions at 0, 90, 180 and 270 degree around the main peak in the centre of the (Hx, Hy) plane of the Ic-H (Hx, Hy) dependence. We have also fabricated triangle shaped junctions and obtained the magnetic field dependence of Josephson current, where sub peaks can be observed in six directions at 0, 60, 120, 180 240 and 300 degree around the centre of the (Hx, Hy) magnetic plane. This magnetic dependence has hexagonal symmetry. We also simulated the dependence assuming the uniform current flow in the junction area. The gauge-invariant-phase-difference between the two superconducting electrodes is modulated perpendicular to the external magnetic field direction inside the barrier region, where the modulation wavelength is inverse proportional to the magnitude of the applied magnetic field. Quite excellent agreement between the measured data and the simulation result has successfully been obtained. (1)Akiyoshi Nakayama, Susumu Abe, Tatsuyuki Morita, Makoto Iwata, and Yusuke Yamamoto, IEEE Trans.Mag.,Vol.36, No.5, pp.3511-3513, Sep.,2000