Unconventional mesophases formed by condensed vector waves in a medium of achiral molecules

A phenomenological theory that describes the phase transitions from a liqui d of achiral molecules to the periodic antiferroelectric mesophases is pres ented. The transitions are shown to be driven by the vector-wave condensati on mechanism. Resulting ordered phases have the structure of a vector wave with linear, circular, or elliptic polarization. The phase diagram, the sta bility with respect to spatial modulation, and the behavior in an external field are discussed in relation with the recently discovered achiral antife rroelectric liquid crystals.