Binysh Jack, Pollard Joseph, Alexander Gareth P
Mathematics Institute, Zeeman Building, University of Warwick, Coventry CV4 7AL, United Kingdom.
Department of Physics, University of Bath, Claverton Down, Bath BA2 7AY, United Kingdom.
Phys Rev Lett. 2020 Jul 24;125(4):047801. doi: 10.1103/PhysRevLett.125.047801.
We describe the geometry of bend distortions in liquid crystals and their fundamental degeneracies, which we call β lines; these represent a new class of linelike topological defect in twist-bend nematics. We present constructions for smecticlike textures containing screw and edge dislocations and also for vortexlike structures of double twist and Skyrmions. We analyze their local geometry and global structure, showing that their intersection with any surface is twice the Skyrmion number. Finally, we demonstrate how arbitrary knots and links can be created and describe them in terms of merons, giving a geometric perspective on the fractionalization of Skyrmions.
我们描述了液晶中弯曲畸变的几何形状及其基本简并性，我们将其称为β线；这些代表了扭曲弯曲向列相中新的一类线状拓扑缺陷。我们给出了包含螺旋位错和刃位错的近晶状织构以及双扭曲和斯格明子的涡旋状结构的构造。我们分析了它们的局部几何形状和全局结构，表明它们与任何表面的交线是斯格明子数的两倍。最后，我们展示了如何创建任意纽结和链环，并用量子色动力学的单极子来描述它们，从而给出斯格明子分数化的几何观点。
