Instability of a lattice semifluxon in a current-biased 0-π array of Josephson junctions

We consider a one-dimensional parallel biased array of small Josephson junctions with a discontinuity point characterized by a phase jump of π in the phase difference. The system is described by a spatially nonautonomous discrete sine-Gordon equation. It is shown that in the infinitely long case there is a semifluxon spontaneously generated attached to the discontinuity point. Comparing the configurations of the semifluxon, we find an energy barrier similar to the Peierls-Nabarro barrier. We calculate numerically the minimum bias current density to overcome this barrier which is a function of the lattice spacing. It is found that the minimum bias current is the critical current for the existence of static lattice semifluxons. For bias current density above the minimum value, the semifluxon changes the polarity and releases 2π fluxons. An analytical approximation to the critical current as a function of the lattice spacing is presented.