Mosaics of topological defects in micropatterned liquid crystal textures.

Topological defects in the orientational order that appear in thin slabs of a nematic liquid crystal, as seen in the standard schlieren texture, behave as a random quasi-two-dimensional system with strong optical birefringence. We present an approach to creating and controlling the defects using air pillars, trapped by micropatterned holes in the silicon substrate. The defects are stabilized and positioned by the arrayed air pillars into regular two-dimensional lattices. We explore the effects of hole shape, lattice symmetry, and surface treatment on the resulting lattices of defects and explain their arrangements by application of topological rules. Last, we show the formation of detailed kaleidoscopic textures after the system is cooled down across the nematic-smectic A phase transition, frustrating the defects and surrounding structures with the equal-layer spacing condition of the smectic phase.