Vortex Street Structure in Chiral Smectic C Liquid Crystal

Chiral smectic C liquid crystal of planar geometry put between two glass plates shows a structure with double of vortex streets. The order parameter characterizing the chiral smectic C phase satisfies an equation similar to the Ginzburg-Pitaevskii equation for liquid helium and its spatial variation is studied. A pitch of smectic C phase is inversely proportional to density of pairs of vortex and anti-vortex, and increases with decreasing plate-separation as a result of competition between chirality of the material and the strain energy due to vortex streets produced by the boundaries. The competition effect leads to the decrease of the transition temperature between smectic A and chiral smectic C phases in agreement with the experimental results.