Department of Physics, Durham University, Durham, DH1 3LE, United Kingdom.
Department of Physics and Centre for Complexity Science, University of Warwick, Coventry, CV4 7AL, United Kingdom.
Phys Rev Lett. 2023 Jun 2;130(22):228102. doi: 10.1103/PhysRevLett.130.228102.
We give a complete topological classification of defect lines in cholesteric liquid crystals using methods from contact topology. By focusing on the role played by the chirality of the material, we demonstrate a fundamental distinction between "tight" and "overtwisted" disclination lines not detected by standard homotopy theory arguments. The classification of overtwisted lines is the same as nematics, however, we show that tight disclinations possess a topological layer number that is conserved as long as the twist is nonvanishing. Finally, we observe that chirality frustrates the escape of removable defect lines, and explain how this frustration underlies the formation of several structures observed in experiments.
我们使用接触拓扑学的方法对胆甾相液晶中的缺陷线进行了完整的拓扑分类。通过关注材料手性所扮演的角色，我们展示了标准同伦理论无法检测到的“紧致”和“过扭曲”的不缠结线之间的基本区别。过扭曲线的分类与向列相相同，然而，我们表明，只要扭曲不为零，紧致不缠结线就具有拓扑层数守恒的性质。最后，我们观察到手性会阻碍可移除缺陷线的逃逸，并解释这种阻碍是如何导致实验中观察到的几种结构的形成的。
