Chirality measure and chiral order parameter for a two-dimensional system

A chirality measure and a chiral order parameter are defined for two-dimensional systems based upon the transformation properties of pseudotensors. The quantities are derived by considering the polarization induced by an electric field applied normal to a system comprising a vacuum above an inhomogeneous dielectric bounded by a plane surface. The quantities are defined by analogy to the three-dimensional case which has been considered by the authors previously. The index is illustrated by a calculation of the chiral order parameter for an Archimedean spiral structure.