Anyonic Defect Braiding and Spontaneous Chiral Symmetry Breaking in Dihedral Liquid Crystals
Anyonic Defect Braiding and Spontaneous Chiral Symmetry Breaking in Dihedral Liquid Crystals
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DOI：
10.1103/physrevx.12.011027
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发表时间：
2020-11
影响因子：
12.5
通讯作者：
Alexander Mietke;J. Dunkel
中科院分区：
文献类型：
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作者：
Alexander Mietke;J. Dunkel
二面角液晶是一种具有k倍离散旋转对称性和反射对称性的微观粒子集合体.推广的半整数缺陷在双折射液晶，二维DLC可以主机点缺陷的分数拓扑电荷$\pm m/k$。从一个通用的微观模型出发，我们得到了一个统一的流体动力学描述的DLCs与对齐和反对齐的短程相互作用的Ginzburg-Landau和Swift-Hohenberg理论的一个普遍的复杂的序参数场。在此框架的基础上，我们证明了在连续介质和粒子模拟绝热编织协议，通过适当的边界条件，可以实现经典对应的任意交换对称性。该理论进一步预测了一种新的自发手性对称性破缺过渡反对齐DLCs，在定量协议与粒子模拟。鉴于二面角胶体的设计和控制组装的最新进展，我们期望这些理论预测可以实现与目前可用的实验技术，从而有望在软物质系统中的分数拓扑信息存储和处理的路径。
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 $\pm m/k$. 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.