Collisions of monopoles, disclinations and dislocations

Abstract

Motions and collisions of topological defects produced during symmetry breaking transitions is a crucial issue in cosmology and in condensed matter physics. Here, we deal with topological defects in nematics and cholesterics. Nematics may contain linear defects i.e. disclinations and point defects i.e. monopoles while cholesterics may contain linear defects of their 1D periodic order parameter, i.e. dislocations. The dowser texture appears as a natural universe of the nematic monopoles. They can be generated in it, set into motion and brought to collisions that may result in annihilation of pairs of monopoles. We show how to generate pairs of disclinations in twisted nematic cells by the isotropic-nematic transition in the presence of magnetic fields. When two such disclinations collide, i.e. enter into a contact at one point, an intercommutation or rewiring into a new pair of disclination can occur. We show how to bring these disclinations to collisions by means of an electric field and how to steer the rewiring by magnetic fields. For generation of dislocations in cholesteric we use a Grandjean–Cano wedge made of crossed cylindrical mica sheets. After their nucleation upon dilation, dislocation loops are growing and collide. Collision of dislocation loops can result in a trivial crossing or may produce a stable configuration called Lehmann cluster. Subsequently, upon application of a high enough tensile strain, the Lehmann splits into a pair of dislocations that can be entangled.