Tensorial Model of Chiral Smectic C Liquid Crystals

We propose a continuum tensorial model for chiral smectic C (SmC^*) liquid crystals using a tensor-valued order parameter Q to describe orientational order and a real-valued order parameter $δρ$ to capture layer modulation. This model accounts for the coupled effects of nematic alignment, smectic layering, chirality and spontaneous polarisation inherent in SmC^* systems. The model is validated through a series of numerical experiments -- helix, bistable switching, bookshelf and chevron, and defect in SmC^*. Our results highlight the model's capability to describe complex phenomena in SmC^* liquid crystals, providing a robust foundation for further theoretical and applied studies on phase transitions.