期刊名称：Proceedings of the National Academy of Sciences
印刷版ISSN：0027-8424
电子版ISSN：1091-6490
出版年度：2014
卷号：111
期号：46
页码：16268-16273
DOI：10.1073/pnas.1405928111
语种：English
出版社：The National Academy of Sciences of the United States of America
摘要：SignificanceThere are few theoretical predictions of knotted, linked, solitonic, and other topologically nontrivial field configurations, which can be tested by experiments, due to the lack of experimentally accessible systems and techniques. This work presents an experimental realization and thorough theoretical analysis of interplay between topologies of the nematic field and closed confining surfaces with systematically varied genus. Handlebody-shaped nematic drops with normal boundary conditions reveal a large diversity of controlled field configurations, including ones with linked and knotted half-integer defect lines that are topologically distinct from predictions of mathematical theorems and that can exist only in nonpolar media. Our model system may become a testbed for probing a scale-invariant interplay of topologies of confining surfaces, fields, and defects. Topologically nontrivial field excitations, including solitonic, linked, and knotted structures, play important roles in physical systems ranging from classical fluids and liquid crystals, to electromagnetism, classic, and quantum field theories. These excitations can appear spontaneously during symmetry-breaking phase transitions. For example, in cosmological theories, cosmic strings may have formed knotted configurations influencing the Early Universe development, whereas in liquid crystals transient tangled defect lines were observed during isotropic-nematic transitions, eventually relaxing to defect-free states. Knotted and solitonic fields and defects were also obtained using optical manipulation, complex-shaped colloids, and frustrated cholesterics. Here we use confinement of nematic liquid crystal by closed surfaces with varied genus and perpendicular boundary conditions for a robust control of appearance and stability of such field excitations. Theoretical modeling and experiments reveal structure of defect lines as a function of the surface topology and material and geometric parameters, establishing a robust means of controlling solitonic, knotted, linked, and other field excitations.
