Liquid crystals as a playground of topological defects

Abstract: Physical fields might be fundamental constituents of nature. Furthermore, topological defects in relevant physical fields might play the role of fundamental particles as first demonstrated by Skyrmy [1]. He introduced topologically protected solitons (referred to as skyrmions) as candidates for mesons and baryons. Therefore, one could explain all natural complexity from the viewpoint of TDs and their assemblies. Liquid crystals (LCs) are particularly adequate to study TDs and related topological phenomena. They exhibit diverse qualitatively different TDs in form of point, line, wall, and texture configurations. In LCs different assemblies of TDs could be relatively easily created, stabilized, manipulated, and observed (e.g., using polarizing microscopy). In the lecture, we will present our studies of different TDs in orientationally ordered LCs that might be analogs of fundamental excitations in nature the behavior of which is still not understood. We demonstrate that geometrical curvature [2] is the mean generic formation and TD stabilization mechanism. We show that the topology of torus stabilizes “chargeless” TDs [3] which might play the role of neutrinos. In LCs they form an elastic ribbon-like structure that embeds the toroidally shaped LC-immersed colloidal particle. Furthermore, we present the formation and stabilization mechanism of merons (skyrmion family members) and their condensation in crystal-like configurations. In pour experiments, we made their structural details and dynamics experimentally accessible by forcing the LC structure close to a critical point, in which the relevant order parameter field correlation length and relaxation time diverge. These quantities dominate the characteristic linear size of the defect core structure and its dynamic features. In particular, we show how TDs mediate temperature-driven order-disorder phase transition in chiral LCs.

[1] T. H. R. Skyrme, A unified field theory of mesons and baryons, Nucl. Phys. 31, 556 (1962). [2] L. Mesarec, W. Góźdź, A. Iglič, S. Kralj, Effective topological charge cancelation mechanism, Sci. Rep. 6, 27117 (2016). [3] S. Harkai, B.S. Murray, C. Rosenblatt, S. Kralj, Electric field driven reconfigurable multistable topological defect patterns, Phys. Rev. Res. 2, 013176 (2020).

mathematical physicsgeneral physicsquantum physics

Audience: advanced learners

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QM Foundations & Nature of Time seminar

Series comments: Description: Physics foundations discussion seminar

Current access link in th.if.uj.edu.pl/~dudaj/QMFNoT

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