Abstract
Dihedral (“k-atic”) liquid crystals (DLCs) are assemblies of microscopic constituent particles that exhibit k-fold discrete rotational and reflection symmetries. Generalizing the half-integer defects in nematic liquid crystals, two-dimensional k-atic DLCs can host point defects of fractional topological charge ±m/k. 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.
| Original language | English |
|---|---|
| Article number | 011027 |
| Number of pages | 23 |
| Journal | Physical Review X |
| Volume | 12 |
| DOIs | |
| Publication status | Published - 9 Feb 2022 |
Bibliographical note
Funding Information:We thank Vili Heinonen, Martin Zwierlein, and Mehran Kardar for helpful discussions and insightful comments. This work was supported by a Longterm Fellowship from the European Molecular Biology Organization (EMBO ALTF 528-2019, A. M.), a Postdoctoral Research Fellowship from the Deutsche Forschungsgemeinschaft (DFG Project No. 431144836, A. M.), a Complex Systems Scholar Award from the James S. Mc-Donnell Foundation (J. D.), and the Robert E. Collins Distinguished Scholarship Fund (J. D.).
Publisher Copyright:
© 2022 authors. Published by the American Physical Society.