Phenomenological theory of the polarized helicoidal smecticCphase

We present a Landau theory of the smectic $A$ to helicoidal smectic $C$ phase transition which has recently been discovered. We analyze qualitatively the molecular interactions between chiral molecules in order to explain the appearance of a twisted smectic $C$ phase. Using an expansion of the free energy, we show how a second-order transition takes place. We also study the properties of the system near the phase change: (i) the behavior of the dielectric susceptibility and piezoelectric coefficient; (ii) the transition to a regular smectic $C$ phase by means of an electric field. Comparison is made with the available experimental results.