Curvature and topology in smectic-A liquid crystals

Abstract

Considerations of rotational invariance in one-dimensionally modulated systems such as smectics-A, necessitate nonlinearities in the free energy. The presence of these nonlinearities is critical for determining the layer configurations around defects. We generalize our recent construction for finding exact minima of an approximate nonlinear free energy to the full, rotationally invariant smectic free energy. Our construction exhibits the detailed connection between mean curvature, Gaussian curvature and layer spacing. For layers without Gaussian curvature, we reduce the Euler–Lagrange equation to an equation governing the evolution of a surface. As an example, we determine the layer profile and free energy of an edge dislocation.