Induced vortex dynamics in parallel Josephson junction arrays

Abstract

As an attempt to understand many unusual characteristics of Josephson junctions between high-${\mathrm{T}}_{\mathrm{c}}$ Cu-oxide superconductors, we employed a parallel Josephson junction array model to study dynamical properties of the high-${\mathrm{T}}_{\mathrm{c}}$ superconducting single grain-boundary Josephson junction, where the relative scale of Josephson penetration depth ${\ensuremath{\lambda}}_{\mathrm{J}}$ is expected to play a crucial role in determination of its dynamics. Results of our numerical studies on the parallel Josephson junction arrays are presented for various values of Ginzburg-Landau parameters ${\mathrm{\ensuremath{\kappa}}}_{\mathrm{J}}$=${\ensuremath{\lambda}}_{\mathrm{J}}$/a, where a represents the array spacing. For the calculations, we take into account the full long-range inductions between vortices and the effects of induced magnetic fields by external currents in the array. From the results, it is found that subharmonic Shapiro steps emerge even under the zero external magnetic field for ${\mathrm{\ensuremath{\kappa}}}_{\mathrm{J}}$\ensuremath{\sim}1, while subharmonic Shapiro steps are suppressed in the limits of either ${\mathrm{\ensuremath{\kappa}}}_{\mathrm{J}}$\ensuremath{\rightarrow}0 or ${\mathrm{\ensuremath{\kappa}}}_{\mathrm{J}}$\ensuremath{\rightarrow}\ensuremath{\infty}. We conclude that, for the intermediate case of ${\mathrm{\ensuremath{\kappa}}}_{\mathrm{J}}$\ensuremath{\sim}1, the edge magnetic fields induced by external currents may be responsible for the existence of subharmonic Shapiro steps with no external magnetic field present.