Abstract
Dihedral (“-atic”) liquid crystals (DLCs) are assemblies of microscopic constituent particles that exhibit -fold discrete rotational and reflection symmetries. Generalizing the half-integer defects in nematic liquid crystals, two-dimensional -atic DLCs can host point defects of fractional topological charge . Starting from a generic microscopic model, we derive a unified hydrodynamic description of DLCs with aligning or antialigning short-range interactions in terms of Ginzburg-Landau and Landau-Brazovskii-Swift-Hohenberg theories for a universal complex order-parameter field. Building on this framework, we demonstrate in particle simulations how adiabatic braiding protocols, implemented through suitable boundary conditions, can emulate anyonic exchange behavior in a classical system. Analytic solutions and simulations of the mean-field theory further predict a novel spontaneous chiral symmetry-breaking transition in antialigning DLCs, in quantitative agreement with the patterns observed in particle simulations.
- Received 10 November 2020
- Revised 8 December 2021
- Accepted 9 December 2021
DOI:https://doi.org/10.1103/PhysRevX.12.011027
Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article’s title, journal citation, and DOI.
Published by the American Physical Society
Physics Subject Headings (PhySH)
Popular Summary
Historically, the subatomic world has been divided into two types of particles—bosons and fermions—depending on how pairs of the particles behave when their positions are swapped. But in 2D materials, there is a third, middle-ground option: the anyon. These quasiparticles have properties that make them attractive for use in quantum computation, but they remain very difficult to create and control. Instead, some researchers turn to analog classical systems with entities that are like anyons but are easier to work with. Here, we mathematically explore anyonic counterparts in a type of 2D liquid crystal.
Specifically, we develop a mathematical model of dihedral liquid crystals, assemblies of positionally disordered but orientationally ordered particles with particular symmetries. These assemblies can have defects—misalignments of neighboring particles—whose positions can be braided around each other by tuning the particle orientations along the boundary of the liquid crystal. By studying the braiding of defect pairs in our liquid-crystal model, we find that the particle orientations within the domain enclosed by the defects acquire changes that are analogous to those of anyonic wave functions.
Broadly, our results provide guidance for implementing anyonic behavior in classical soft-matter systems with suitably designed particle interactions. Promising candidates for future experimental realizations could be certain types of colloids or thin films of molecules.
