Twisted and frustrated states of matter

The World, and much of Nature that we see within it, experiences an environment of reduced symmetries. For example, living organisms are dependent on asymmetric or dissymmetric structures for their life processes. In the solid state, a large number of space groups are chiral. Conversely, in liquids, the effects of reduced symmetries are smeared out owing to the dynamical fluctuations of the constituent molecules, atoms or ions. Thus, on progressing from the strongly ordered solid to the amorphous liquid state, the effects of reduced symmetries weaken as the molecular or atomic correlations and penetration lengths fall. Between these two states of matter, the fourth state of organized fluids can be markedly affected by chirality, and over substantial length scales, owing to both the fluidity and partial ordering of the molecules. In effect, complex fluids can amplify the effects of chirality at the molecular level. Broken symmetries in self-organizing systems can lead to the formation of novel phases of matter and to the creation of structured liquids, and to the generation of nonlinear properties such as heli-, ferro-, ferri- and antiferro-electricity, and electroclinism, which can be harnessed in a wide range of applications including thermal sensors, imaging devices and information displays, to name but a few.