DYNAMICS OF A TWO-DIMENSIONAL JOSEPHSON JUNCTION

摘要

The aim of the paper is the determination of static and dynamic processes in a two-dimensional Josephson junction via numerical solution of 2+1 dimensional sine-Gordon equation (sGe) with suitably chosen boundary conditions. The model we adopt bases on the assumption that the normal derivative of the phase order parameter on the border of a junction (a function) is given by the surface current distribution on superconductive electrodes. For simplicity, the electrodes are assumed to be homogeneous with respect to the coordinate perpendicular to the plane of a junction. The surface current distribution and the effects of externally applied magnetic field constitute then a linear problem. Thus the boundary conditions for a nonlinear problem (sGe) are imposed by the solution of this trivial, linear problem. We are going to present the static and dynamic Josephson current paterns for different values of a biasing current, an external magnetic field, its orientation and for rectangular and circular junction cross-sections. When the biasing current (or an external magnetic field) is sufficiently strong, the processes become periodic in time, revealing a flux creep originated from junction corner. Moreover, there is a numerical confirmation of the fact that de-voltage across a junction does not depend on space coordinates.