Mobile π-kinks and half-integer zero-field-like steps in highly discrete alternating 0-π Josephson junction arrays

The dynamics of a one-dimensional, highly discrete, linear array of alternating 0- and π-Josephson junctions is studied numerically, under constant bias current at zero magnetic field. The calculated current-voltage characteristics exhibit half-integer and integer zero-field-like steps for an even and an odd total number of junctions, respectively. Inspection of the instantaneous phases reveals that, in the former case, single π- kink excitations (discrete semi-fluxons) are supported, whose propagation in the array gives rise to the 1/2-step, while in the latter case, a π-kink-π-antikink pair appears, whose propagation gives rise to the 1-step. When additional 2π- kinks are inserted in the array, they are subjected to fractionalization, transforming themselves into two closely spaced π-kinks. As they propagate in the array along with the single π-kink or the π-kink-π-antikink pair, they give rise to higher half-integer or integer zero-field-like steps, respectively.