Topological Solitons in Liquid Crystals and Colloids

University Of Colorado At Boulder, Boulder CO

Investigators

Abstract

NON-TECHNICAL ABSTRACT Colloids are abundant in nature, science and technology, with examples ranging from milk to quantum dots that are of interest for quantum computing. Similarly, liquid crystal ordering is important in contexts ranging from biological membranes to displays in consumer devices. In every pixel of a liquid crystal display, the direction of rod-like molecules is rotated by a low-voltage electric field, so that the transmitted light can be controlled to convey information at will. This facile electric switching, which is at the heart of $500 billion per year global liquid crystal industry, deals with very simple uniform and continuously distorted structures of the molecular alignment field of rod-like molecules. The PI and his team study how liquid crystals can be controlled to host knotted patterns of this molecular alignment field. They study tiny rod-like and disc-like colloidal particles dispersed in a liquid crystal to develop a "recipe book" for organizing particles into precisely controlled structures. Electric and magnetic fields can interact with these structures, knotting or unknotting them, which may enrich the means of controlling light by liquid crystals. This research may lead to applications of importance to society, such as new breeds of displays, beam steering and data storage devices. PI combines this research with a broad range of synergistic educational and outreach activities, including shows and science tours for school teachers and students, advising student chapters of professional societies, providing research experiences for students from minority-serving institutions, advising undergraduate and PhD researchers, teaching conference courses for liquid crystal industry, participation in visiting lecturer programs and organization of conferences and summer schools. TECHNICAL ABSTRACT PI explores the fundamental organizing principles behind topology-dictated self-assembly of anisotropic liquid crystal molecules and colloidal nanoparticles into topologically distinct soliton configurations that are thousands-to-millions times larger than molecules and nanoparticles. Widely studied magnetic skyrmions are 2D solitons with a spatially localized topology-protected continuous winding of magnetization. 3D skyrmions (hopfions) are localized in all three spatial dimensions and characterized by the Hopf index, a topological invariant with a geometric interpretation of the linking number of any two closed-loop preimages, regions in space with the same orientation of field corresponding to a single point on the order parameter space, such as a unit sphere for the magnetization vector field. PI develops a new breed of tunable liquid crystal structures with complex but predictable topology-dictated response to external fields and propagating optical solitons and vortices of laser beams. Both equilibrium self-assembly and dynamic interactions between 2D and 3D solitons are controlled and probed using a combination of laser tweezers, 3D nonlinear optical imaging, and video microscopy. This interdisciplinary work addresses key problems at the interfaces of condensed matter physics, topology, nanoscience and photonics. The emerging scientific frontiers at the nexus of these fields show exceptional promise of new discovery and applications. This work advances our fundamental knowledge of structure and dynamics of 3D topological solitons, expands the diversity of self-assembly phenomena in complex fluids and impinges on fundamental knowledge in scientific fields as diverse as colloidal interactions, topology, nonlinear and singular optics, all optical information processing, and other. In addition to serving as a model system for fundamental studies, potential technological uses of the studied solitons include beam steering devices, generators of optical vortices for singular optics applications, optical circuitry with robust capabilities of controlling polarization of light, and topologically nontrivial solitons with knotted field configurations forming crystalline and other lattices in materials. Building on his past education and outreach accomplishments, the PI integrates this research with a broad spectrum of synergistic activities, ranging from training of students and teaching courses for non-scientists to conveying the scientific excitement to public and children through the University of Colorado Saturday Physics Lectures and Wizard Shows. This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria.