Anyonic defect braiding and spontaneous chiral symmetry breaking in dihedral liquid crystals

Abstract

Dihedral 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 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 and anti-aligning short-range interactions in terms of Ginzburg-Landau and Swift-Hohenberg theories for a universal complex order-parameter field. Building on this framework, we demonstrate in both continuum and particle simulations how adiabatic braiding protocols, implemented through suitable boundary conditions, can realize classical counterparts of anyonic exchange symmetries. The theory further predicts a novel spontaneous chiral symmetry breaking transition in anti-aligning DLCs, in quantitative agreement with particle simulations. In view of recent advances in the design and controlled assembly of dihedral colloids, we expect that these theoretical predictions can be realized with currently available experimental technology, thereby promising a path to fractional topological information storage and processing in soft matter systems.

Hydrodynamic theory of $p-$atic liquid crystals

“…For the past four decades, the hexatic phase and KTHNY melting scenario have been subject to extensive theoretical and experimental investigation, aimed at clarifying the nature of the individual solid-hexatic and hexatic-isotropic phase transitions, as well as the role of material properties. Large-scale numerical simulations [6,7], experiments with superparamagnetic colloids [8,9] and, more recently, tilted monolayers of sedimented colloidal hard-spheres [10], in particular, have progressively shed light on several fascinating aspects of these transitions, while opening new avenues in condensed matter physics at the interface between statistical mechanics, material science and topology [11][12][13][14][15][16]. By contrast, the hydrodynamic behavior of hexatics has received little attention and, with the exception of a small number * giomi@lorentz.leidenuniv.nl of pioneering works, e.g.…”

Non-orientable order and non-Abelian response in frustrated metamaterials

“…Our metamaterials escape the traditional classification of order by symmetry breaking. Considering more general stress distributions, we leverage non-orientable order to engineer robust mechanical memory [5][6][7][8][9][10][11] and achieve non-Abelian mechanical responses that carry an imprint of the braiding of local loads [12,13]. We envision this principle to open the way to designer materials that can robustly process information across multiple areas of physics, from mechanics to photonics and magnetism.…”