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 even and 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 pair of $π-$kink -- $π-$antikink 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.

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