  Chiral liquid crystals exhibit in-plane spontaneous polarizations, however in
their smectic phase the primary order parameter is a tilt vector associated
with molecular rotations around the long molecular axis parallel to the
director. The molecular rotations lead to several distinct phases among which a
domain-wall texture with a periodic-kink soliton profile. In this study the
formation of domain walls in smectic chiral liquid crystals is analyzed, with
emphasis on the competition between ising-type symmetric and antisymmetric
nearest-neighbor interactions, and an in-plane electric field. It is found that
antisymmetric intermolecular interactions, which are of chiral origin, increase
the width of kink structures in the domain wall at moderate intensity of the
$y$ component of the electric field. Increasing the $x$ component of the
electric field creates unstable condition for soliton formation irrespective of
magnitudes of the symmetric and chiral intermolecular interactions. Stability
condition for single-kink domain-wall structures in the discrete molecular
chain, is discussed by estimating the Peierls stress experienced by the
single-kink soliton. Results suggest that chirality lowers the Peierls-Nabarro
barrier, hence increasing the lifetime of single-kink structures in the
discrete medium.
