Defects in liquid crystals

Defects are local breakings of symmetry in an ordered medium. The physics of defects has long been reduced to the study of dislocations in solids, and to the main physical phenomena they are responsible for, like plastic deformation. Dislocations break translational symmetries. Disclinations break rotational symmetries and are the basic defects of media with continuous symmetries, like liquid crystals. In this review, it is stressed how their study has contributed to a renewal of the physics of defects. Static and dynamic properties in the nematic, cholesteric, blue, smectic and columnar phases of liquid crystals are described in detail, up to the most recent results, for small-molecule thermotropic liquid crystals as well as for lyotropic and polymeric liquid crystals. The authors also discuss the homotopy classification of defects, including point defects, and compare it with the Volterra classification; finally they present the curved-crystal description of frustration in the light of the relevant situation in liquid crystals. The usefulness of the concepts introduced for liquid crystals for the study of other systems (structural problems in biology, dissipative structures, magnetic domains, etc.) is also emphasised.