Topological Defect Network in Nematic Liquid Crystal Generated by Patterned Electrodes

Topological defects arise when the symmetry in liquid crystal (LC) is broken during phase transitions or under application of an electric field. Usually they are unwanted in LC displays and optical devices, because they introduce unevenness of the LC distribution. However, resent researches revealed that topological defects and disclinations can attract micro-particles and biological molecules to build self-assembled micro-wires [1] and tissues [2]. The defect itself can generate optical vortex for quantum informatics. Huddles of defects scatter light, so they can be utilized as smart windows [3]. All of the fascinating applications will be realized only if the type and position of defects can be precisely controlled. Techniques to generate defects using patterned surface alignment [4] or 3D micro-structures [5] has been developed, but methods based on patterned electrodes has never been discussed. We will present the topological defect network in nematic LC generated by patterned electrodes (Fig. 1). Type, number, size and position of defects can be precisely controlled by the delicately designed electric field. Defects and their network can be switched on and off by application of electric field. Large defect network can be stable if the sum of its index of vertices and the geometry of the boundary obey Poincaré-Hopf (for planar surface alignment) or Stein-Gauss theorems (for homeotropic surface alignment). Topological defects will be arranged in cubic or hexagonal lattices (Fig. 2). Feasible combination of topological charges is determined by the rotational symmetry, reflectional symmetry, and the lattice structure. Selection rules for stable defect combinations will be established based on the topological rules and symmetries mentioned above. Stable defect network will be demonstrated by simulations and test cell experiments.