Review: knots and other new topological effects in liquid crystals and colloids
Review: knots and other new topological effects in liquid crystals and colloids
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DOI：
10.1088/1361-6633/abaa39
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发表时间：
2020-07
影响因子：
18.1
通讯作者：
I. Smalyukh
中科院分区：
文献类型：
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作者：
I. Smalyukh
几千年来，人类一直痴迷于宗教、文化和日常生活中的结，而像高斯、开尔文和马克斯韦尔这样的物理学家在几个世纪前就已经将它们纳入模型中。如今，胶体颗粒可以被制成具有任意复杂程度的结节和链节的形状。在液晶中，通过使用胶体粒子和激光镊子，以及将向列相流体限制为具有复杂拓扑结构的微米大小的液滴，可以将奇异涡旋线的闭合环结在一起。打结和连接的胶体粒子产生奇异缺陷的结和链，这些缺陷可以与胶体粒子结相连(或不相连)，揭示了结合场的拓扑结构和胶体物体的拓扑非平凡表面之间相互作用的多样性。在液晶和胶体铁磁体的非奇异分子排列和磁化场中，甚至出现了更多不同的打结结构。拓扑孤子包括Hopfions、Skyrmion、Heli扣、Torons等空间局域连续结构，这些结构是根据同伦理论分类的，具有整数值拓扑不变量，通常包含结节或链接的前像，即空间中对应于序参数空间的单点的非奇异区域。液晶、胶体和铁磁体中的一大批拓扑孤子有望带来新的信息显示品种，以及大量的数据存储、电光和光子应用。它们像粒子一样的集体动力学与活动物质中的相干运动相呼应，从人群到鱼群不等。这篇综述讨论了这一领域的最新进展，以及在打结软物质物理学方面的最新进展和有待解决的问题。我们系统地概述了节状场的配置，它们之间允许的变换，它们的物理稳定性，以及如何使用一种形式的节状场来模拟、创建和印记其他形式。液晶和胶体可获得的各种对称性提供了对具有基础和应用重要性的完全非奇异场和奇异场的稳定性、变换和紧急动力学的洞察。这篇评论的共同主线是能够在真实空间中以实验的方式可视化这些结。综述最后讨论了液晶和胶体中纽结的研究如何为其他物理学分支中与拓扑相关的结构提供见解，并回答了许多悬而未决的问题，以及这些通过实验观察到的纽结如何具有为数学纽结理论提供新灵感的强大潜力。
Humankind has been obsessed with knots in religion, culture and daily life for millennia, while physicists like Gauss, Kelvin and Maxwell already involved them in models centuries ago. Nowadays, colloidal particles can be fabricated to have shapes of knots and links with arbitrary complexity. In liquid crystals, closed loops of singular vortex lines can be knotted by using colloidal particles and laser tweezers, as well as by confining nematic fluids into micrometer-sized droplets with complex topology. Knotted and linked colloidal particles induce knots and links of singular defects, which can be interlinked (or not) with colloidal particle knots, revealing the diversity of interactions between topologies of knotted fields and topologically nontrivial surfaces of colloidal objects. Even more diverse knotted structures emerge in nonsingular molecular alignment and magnetization fields in liquid crystals and colloidal ferromagnets. The topological solitons include hopfions, skyrmions, heliknotons, torons and other spatially localized continuous structures, which are classified based on homotopy theory, characterized by integer-valued topological invariants and often contain knotted or linked preimages, nonsingular regions of space corresponding to single points of the order parameter space. A zoo of topological solitons in liquid crystals, colloids and ferromagnets promises new breeds of information displays and a plethora of data storage, electro-optic and photonic applications. Their particle-like collective dynamics echoes coherent motions in active matter, ranging from crowds of people to schools of fish. This review discusses the state of the art in the field, as well as highlights recent developments and open questions in physics of knotted soft matter. We systematically overview knotted field configurations, the allowed transformations between them, their physical stability and how one can use one form of knotted fields to model, create and imprint other forms. The large variety of symmetries accessible to liquid crystals and colloids offer insights into stability, transformation and emergent dynamics of fully nonsingular and singular knotted fields of fundamental and applied importance. The common thread of this review is the ability to experimentally visualize these knots in real space. The review concludes with a discussion of how the studies of knots in liquid crystals and colloids can offer insights into topologically related structures in other branches of physics, with answers to many open questions, as well as how these experimentally observable knots hold a strong potential for providing new inspirations to the mathematical knot theory.