Spontaneous cholesteric phase in ferroelectric nematic liquid crystals: Preference for integer number of pitches

In a ferroelectric nematic liquid crystal, the electrostatic interaction can induce a spontaneous cholesteric helix, even if the material is not chiral. If the liquid-crystal cell is infinitely thick, then the predicted pitch depends continuously on material parameters. Here, we consider how the prediction must be modified in a cell of finite thickness. If the Debye screening length is large enough, we find that the free energy has multiple minima. In these minima, the cholesteric pitch is locked to the cell thickness, so that the cell contains an integer number of pitches. However, if the screening length is smaller, then the cholesteric pitch can vary continuously.