The thesis covers complex line defect structures in a uniaxial nematic phase, bound by a planparallel geometry, and the different methods of reconfiguring them. We describe the nematic structures on a mesoscopic scale with a tensor nematic order parameter. Equilibrium states are determined through numerical minization of the corresponding free energy. We enforce different defect structures topologically using boundary conditions on enclosing surfaces, through which we enforce two-dimensional (2D) surface defects, characterized with a winding number m. The boundary conditions are experimentally reproducible with methods such as AFM scribing. We pay special attention to the so-called topologically "chargeless" |m| = 1/2 disclinations, whose 3D topological charge is equal to 0.
First we study the structural diversity enabled by an m = 1 defect enforced by the surface. Depending on the ratio between the cell thickness and biaxial correlation length or the starting conditions, either an m = 1 line defect, a split defect, comprised of two mutually repulsive m = 1/2 lines, or a defect-less escaped structure is realized. We investigate the stability of equilibrium nematic structures and switching between them using an external electric field, which we verify experimentally.
We stabilize the mostly antiparallel "chargeless" lines using a 2×2 pattern of alternating m = ±1/2 surface defects in thick enough cells. We show that such antiparallel disclinations behave like a defect and antidefect with a tendency to mutually annihilate. We demonstrate the possibility of rewiring between different defect structures using an external electric field. By enforcing a 4 × 4 pattern of m = ±1 alternating defects on the master surface, creating a multistable system with 18 quantitatively and 7 qualitatively (meta)stable configurations in thick enough cells. We demonstrate the ability to reversibly switch in select cases using an external electric field, which we qualitatively reproduce experimentally. We show the possibility of stabilizing "chargeless" disclinations using colloids with toroidal topology. Topologically "chargeless" disclinations exhibit properties, similar to Majorana particles. The results are interesting for fundamental and applicative reasons. The different defect configurations that we enforce using the regular patterns of 2D imprinted defects can potentially form loops of periodic 3D structures, which can be useful for various photonic or electro-optic applications.
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