Liquid Crystals under Topologically Non-Trivial Confinement

Handle-Body Nematic Droplet Topologically non-trivial field excitations, including the ones carrying linked and knotted structures, play important roles in many physical systems ranging from classical fluids to liquid crystals, plasmas, electromagnetism, and to fundamental quantum fields. These excitations can appear spontaneously during symmetry breaking phase transitions. For example, in cosmological theories cosmic strings may have formed knotted configurations influencing the Early Universe development while in liquid crystals transient knotted defect lines are observed during isotropic-to-nematic transition. In the latter case knotted topological defects appear spontaneously and are transient non-equilibrium field configurations, which eventually relax to equilibrium defect-free states.

In collaboration with the experimental group of Prof. Smalyukh at the University of Colorado Boulder we explore how topologically non-trivial spatial confinements can be used in order to achieve a robust control of the appearance and stability of topological field excitations. In order to achieve this goal, we use a nematic liquid crystal as a model system and confine it by topologically non-trivial surfaces with systematically varied genus. This allows to generate topological defects of the desired total hedgehog charge which obeys predictions of the Gauss-Bonnet and Poincare-Hopf index theorems. Complementary theoretical calculations and experimental observations reveal non-trivial structures and transformations of defect lines as a function of the surface topology and material and geometric parameters, establishing a robust means of controlling solitonic, knotted, linked and other field excitations. Since few theoretical predictions of topological field configurations can be tested experimentally due to lack of experimentally accessible systems and techniques, our model system may become a testbed for probing a potentially scale-invariant interplay of topologies of confining surfaces, fields, and defects. Similar to probing the cosmological Kibble mechanism using liquid crystal phase transitions, it may enable new cosmology and particle physics relevant experiments.
 
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