Programming Emergent Chiral and Polar Symmetries with Saddle-Splay Elasticity

Emergent chiral symmetries in liquid crystals (LCs) are usually achieved by symmetry breaking in close boundary confinements. Gaining precise control over the location, creation and manipulation of broken symmetries remains a formidable challenge. In this work, we achieve pre-programming of broken chiral symmetries in the nematic phase of two achiral LCs (5CB and 8CB) through a ubiquitous but oft-neglected property of LCs: the “saddle-splay” elasticity. Using combinations of lithographic patterning and selective surface functionalization, we create surface patterns with spatially defined geometry and precisely controlled surface chemistry. Through this, we characterize broken symmetry regimes on a variety of surface patterns, including arrays of circular, trefoil, and annulus posts, in which saddle splay-driven effects gain physical expression. In turn, we unlock the resultant director field patterns, and identify spontaneously broken symmetries within domains exhibiting chiral and polar regimes. By fine-tuning the patterning geometry, we then program the location, energy landscape, and means of manipulation of the symmetry breaking processes. As a result, we demonstrate a multi-state stable LC display device that can be switched at an extremely low voltage density (~0.5 V/µm).