Classification of Defects in Liquid Crystals

Abstract

A tutorial introduction is presented into the notion of “defects” or “singularities” in liquid crystals or, generally, ordered media. It starts from the concept of an order parameter, which is element of a vector space, and from a free energy in terms of Landau-theory. The subset of the vector space, where the free energy takes its minima, is the relevant manifold, whose topological properties determine the defect structure. The topological defect classification is illuminated by several examples of two- and three-dimensional liquid crystals. Also the terms “texture” and “topological solitons” are being addressed.