Chiral Symmetry Breaking and Pattern Formation in Two-Dimensional Films

Thin films of organic molecules, such as Langmuir monolayers and freely suspended smectic films, can exhibit a spontaneous breaking of chiral symmetry. This chiral symmetry breaking can occur through at least three possible mechanisms: (1) the relation between tilt order and bond-orientational order in a tilted hexatic phase, (2) a special packing of non-chiral molecules on a two-dimensional surface, and (3) phase separation of a racemic mixture. Because the chiral order parameter is coupled to variations in the direction of molecular tilt, chiral symmetry breaking leads to the formation of patterns in the tilt direction with one-dimensional or two-dimensional order. Using a Landau theory, we investigate these patterns and predict the critical behavior near the chiral symmetry breaking transition.