Selection Rules for a Stable Large-scale Topological Defect Array in Nematic Liquid Crystals Jieh-Wen Tsung ^{1*}, Ya-Zi Wang^{1}, Bo-Yao Chen^{1}, Sheng Kai Yao^{1}, Shih-Yu Chao^{1}, Jing-Kai Chou^{1}^{1}Department of Electrophysics, National Chiao-Tung University, Hsinchu, Taiwan* Presenter:Jieh-Wen Tsung, email:jwtsung@nctu.edu.tw Orientation of nematic liquid crystal (NLC) around a topological defect is expressed by the equation, ψ=sψ+φ
_{0}, where ψ, s, φ, and φ_{0} are the director spatial phase, topological charge, azimuthal angle, and a spatial phase shift, respectively. Conventionally, defect array is modeled by simply adding the ψ fields of all the defects. The resultant array is a combination of the defects imposed by design (ψ_{s}) and the defects due to the lattice geometry (ψ_{g}). However, defect arrays generated in homeotropic confinement show hyperbolic hedgehogs (ψ_{h}) between the ψ_{s}s, which are out of the scope of the conventional model. In this research, two-dimensional defect 'crystals' with various lattice structures (square and hexagonal), various defect shapes (radial or circular), and various lattice constants (pixel size) are generated by pixelated patterned electrodes in homeotropic NLC cells. The results verify the two selection rules, 1) The total s must be zero, 2) φ_{0} must be a constant throughout the array, and a new model composed of ψ_{s}, ψ_{g} and ψ_{h} is established. Calculation proves that the selected array has minimum free energy. The ψ_{s}-ψ_{g}-ψ_{h} model is versatile and easy to apply, which benefits the design of new topological defect arrays for precision optics, elastomer actuators, and self-assembled microstructure.Keywords: nematic liquid crystal, topological defect, long-range order, homeotropic alignment, topological defect array |