Topological defects in nematics: fundamentals and applications

Abstract

Topological defects (TDs) constitute topologically protected frustrated regions in a host field of an ordered manifold. They are ubiquitous in nature and appear at all scales, including the realms of particle physics, condensed matter, cosmology… The sole condition for their existence is symmetry-breaking. For example, the first theory of phase transition quench-driven coarsening of TDs was developed in cosmology to model events in the early inflationary universe. Furthermore, it might be that localized TDs represent fundamental particles of the Standard Model if relevant physical fields constitute fundamental natural entities. Due to their topological origin, TDs exhibit several universalities. Therefore, it is of interest to identify systems where TDs are easily experimentally accessible, enabling detailed and well-controlled analysis of their universal behavior, cross-fertilizing knowledge in different areas of physics. In this respect liquid crystals (LCs) represent an ideal experiment testbed to study TDs. LCs display numerous phases and structures reached via continuous symmetry breaking phase transition, which can host a rich diversity of TD structures. Furthermore, LCs possess a unique combination of liquid character, orientational and/or translational order, softness (capability to respond strongly to even weak stimuli1), and optical anisotropy and transparency. This symbiosis of properties allows relatively ease of TDs creation, their simple observation (e.g., using polarizing microscopy), stabilization and manipulation of their configurations. Note that, in general, it is difficult to stabilize TDs because they are energetically costly. In this presentation I will show our investigations of TDs in the nematic uniaxial phase, representing the simplest LC configuration, displaying only orientational order. Despite its simplicity, the nematic phase exhibits a rich diversity of defect configurations. We demonstrate that a simple plane parallel cell that confines a nematic LC could host diverse complex and multistable configurations of TDs, which we stabilized using the AFM scribing method2. These competitive states could be reversibly and robustly reconfigured by appropriate external electric fields. Furthermore, we show that complex lattices of line defects, which are otherwise unstable or stable in a narrow interval of temperatures, could be stabilized efficiently by doping LCs with appropriate nanoparticles, owing to the universal defect core displacement mechanism3. We demonstrate that such TD configurations have potential for diverse applications, particularly in nano- and biotechnology: e.g., for nanotechnology-based devices based on reconfigurable conducting nanowires, tunable photonic devices, sensitive sensors… Furthermore, our study of TDs might provide some insight into still unresolved problems of fundamental physics. Namely, LCs could exhibit so-called “chargeless” twist disclinations, which commonly decay into a defectless state. Twist TDs could simultaneously act as defects and antidefects3, and such neighboring pairs could be mutually annihilated. These configurations bear some resemblance to intriguing Majorana particles that, furthermore, could play the role of neutrinos, the physics of which is still unresolved. We show that isolated twist loops could be stabilized by toroidal topology. The latter possesses regions exhibiting positive and negative Gaussian curvature. 2D studies4,5 reveal that such regions attract TDs exhibiting positive and negative topological charges, respectively. Our preliminary investigations reveal that similar mechanisms also could be applied in 3D.