Tetrahedral Order in Banana Liquid Crystals

Bent-core liquid crystal molecules can exhibit phases that require a third-rank symmetric-traceless tensor order parameter, as well as a vector order parameter and the usual second-rank nematic order parameter. The combination gives rise to a rich variety of spatially homogeneous phases ranging from the well-known nematic to novel tetrahedratic and chiral liquids. I discuss experimental signatures of these phases and phase transitions between them.\\[0.3cm] L. Radzihovsky and T.C. Lubensky, Europhys. Lett.54, 206 (2001); Phys. Rev.E 66, 031704 (2002).