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Topological line defects are ubiquitous in nature and appear at all physical scales, including in condensed matter systems, nuclear physics, and cosmology. Particularly useful systems to study line defects are nematic liquid crystals (LCs), where they describe singular or nonsingular frustrations in orientational order and are referred to as disclinations. In nematic LCs, line defects could be relatively simply created, manipulated, and observed. We consider cases where disclinations are stabilized either topologically in plane-parallel confinements or by chirality. In the former case, we report on studies in which defect core transformations are investigated, the intriguing dynamics of strength disclinations in LCs exhibiting negative dielectric anisotropy, and stabilization and manipulation of assemblies of defects. For the case of chiral nematics, we consider nanoparticle-driven stabilization of defect lattices. The resulting line defect assemblies could pave the way to several applications in photonics, sensitive detectors, and information storage devices. These excitations, moreover, have numerous analogs in other branches of physics. Studying their universal properties in nematics could deepen understanding of several phenomena, which are still unresolved at the fundamental level. 

Nematic cells patterned with square arrays of strength m = ±1 topological defects were examined as a function of cell thickness (3 < h < 7.5 μm), temperature, and applied voltage. Thicker cells tend to exhibit an escape or partial escape of the nematic director as a means of mitigating the elastic energy cost near the defect cores, whereas thinner cells tend to favor splitting of the integer defects into pairs of half-integer strength defects. On heating the sample into the isotropic phase and cooling back into the nematic, some apparently split defects can reappear as unsplit integer defects, or vice versa. This is consistent with the system’s symmetry, which requires a first order transition between the two relaxation mechanisms. 

Using a Landau–de Gennes approach, we study the impact of confinement topology, geometry and external fields on spatial positioning of nematic topological defects (TDs). In quasi two-dimensional systems we demonstrate that confinement enforced total topological charge m>>1 decays into elementary TDs bearing charge m=1/2. These assemble close to the bounding substrate to enable essentially bulk-like uniform nematic ordering in the central part of a system. This effect is reminiscent of the Faraday cavity phenomenon in electrostatics. We observe that in certain confinement geometries, varying the order parameter correlation length size could trigger global rotation of an assembly of TDs. Finally, we show that an external electric field could be used to drag the boojum finger tip towards a confinement cell interior. Assemblies of TDs could be exploited as traps for appropriate nanoparticles, opening several opportunities for development of functional nanodevices.