Theory of Polar Blue Phases

In liquid crystals, if flexoelectric couplings between polar order and director gradients are strong enough, the uniform nematic phase can become unstable to formation of a modulated polar phase. Previous theories have predicted two types of modulation, twist-bend and splay-bend; the twist-bend phase has been found in recent experiments. Here, we investigate other types of modulation, using lattice simulations and Landau theory. In addition to twist-bend and splay-bend, we also find polar blue phases, with 2D or 3D modulations of both director and polar order. We compare polar blue phases with chiral blue phases, and discuss opportunities for observing them experimentally.