Solitons in a discrete model of chiral liquid crystals with competing interactions

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.