Chiral symmetry breaking in Langmuir monolayers and smectic films

Langmuir monolayers and freely suspended smectic films can exhibit a spontaneous breaking of chiral symmetry. The order parameter that characterizes this symmetry breaking is coupled to variations in the direction of molecular tilt. As a result, chiral symmetry breaking leads to the spontaneous formation of complex equilibrium patterns with either 1D or 2D modifications in the direction of molecular tilt. A Landau theory for this pattern formation gives a general phase diagram, which includes a uniform nonchiral phase, a striped pattern, a square lattice, and a uniform chiral phase.