Order and frustration in chiral liquid crystals

This article reviews the complex ordered structures induced by chirality in liquid crystals. In general, chirality favours a twist in the orientation of liquid-crystal molecules. In some cases, as in the cholesteric phase, this favoured twist can be achieved without any defects. More often, the favoured twist competes with applied electric or magnetic fields or with geometric constraints, leading to frustration. In response to this frustration, the system develops ordered structures with periodic arrays of defects. The simplest example of such a structure is the lattice of domains and domain walls in a cholesteric phase under a magnetic field. More complex examples include defect structures formed in two-dimensional films of chiral liquid crystals. The same considerations of chirality and defects apply to three-dimensional structures, such as the twist-grain-boundary and moire phases.