  The smectic C (smC) phase represents a unique class of liquid crystal phases
characterised 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., PRL, 126, 177801 (2021)], we propose a new
continuum mathematical model for smC (and smA) by introducing a novel 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 (TFCDs). These results also
reveal the phenomenological differences between smA and smC configurations.
