Chiral symmetry breaking and the soliton-stripe pattern in Langmuir monolayers and smectic films

Chiral symmetry breaking in Langmuir monolayers and smectic films may be modelled by a system of two coupled fields: a scalar field that represents the chirality of the molecules and a vector field that represents the tilt direction of the molecules. In a particular parameter range, we prove the existence of a soliton-stripe pattern using the Gamma-limit theory in perturbative variational calculus. This pattern, modelled by one-dimensional local minimizers of the free energy of the system, consists of stripes of molecules with distinct chirality in the film delineated by sharp domain walls.