A simple tensorial theory of smectic C liquid crystals

Abstract

The smectic C (smC) phase represents a unique class of liquid crystal phases characterized by the layered arrangement of molecules with tilted orientations with respect to layer normals. Building upon the real-valued tensorial smectic A (smA) model in Xia et al. [Phys. Rev. Lett. 126, 177801 (2021)10.1103/PhysRevLett.126.177801], we propose a continuum mathematical model for smC (and smA) by introducing a coupling term between the real tensor containing orientational information and density variation to control the tilt angle between directors and the layer normal (the tilt angle is zero for smA and nonzero for smC). To validate our proposed model, we conduct a series of two- and three-dimensional numerical experiments that account for typical structures in smectics: chevron patterns, defects, dislocations, and toroidal focal conic domains. These results also reveal the phenomenological differences between smA and smC configurations.