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Liquid crystals are complex fluids that allow exquisite control of light propagation thanks to their orientational order and optical anisotropy. Inspired by recent advances in liquid-crystal photo-patterning technology, we propose a soft-matter platform for assembling topological photonic materials that holds promise for protected unidirectional waveguides, sensors, and lasers. Crucial to our approach is to use spatial variations in the orientation of the nematic liquid-crystal molecules to emulate the time modulations needed in a so-called Floquet topological insulator. The varying orientation of the nematic director introduces a geometric phase that rotates the local optical axes. In conjunction with suitably designed structural properties, this geometric phase leads to the creation of topologically protected states of light. We propose and analyze in detail soft photonic realizations of two iconic topological systems: a Su–Schrieffer–Heeger chain and a Chern insulator. The use of soft building blocks potentially allows for reconfigurable systems that exploit the interplay between topological states of light and the underlying responsive medium.
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Topology in soft and biological matter
The last years have witnessed remarkable advances in our understanding of the emergence and consequences of topological constraints in biological and soft matter. Examples are abundant in relation to (bio)polymeric systems and range from the characterization of knots in single polymers and proteins to that of whole chromosomes and polymer melts. At the same time, considerable advances have been made in the description of the interplay between topological and physical properties in complex fluids, with the development of techniques that now allow researchers to control the formation of and interaction between defects in diverse classes of liquid crystals. Thanks to technological progress and the integration of experiments with increasingly sophisticated numerical simulations, topological biological and soft matter is a vibrant area of research attracting scientists from a broad range of disciplines. However, owing to the high degree of specialization of modern science, many results have remained confined to their own particular fields, with different jargon making it difficult for researchers to share ideas and work together towards a comprehensive view of the diverse phenomena at play. Compelled by these motivations, here we present a comprehensive overview of topological effects in systems ranging from DNA and genome organization to entangled proteins, polymeric materials, liquid crystals, and theoretical physics, with the intention of reducing the barriers between different fields of soft matter and biophysics. Particular care has been taken in providing a coherent formal introduction to the topological properties of polymers and of continuum materials and in highlighting the underlying common aspects concerning the emergence, characterization, and effects of topological objects in different systems. The second half of the review is dedicated to the presentation of the latest results in selected problems, specifically, the effects of topological constraints on the viscoelastic properties of polymeric materials; their relation with genome organization; a discussion on the emergence and possible effects of knots and other entanglements in proteins; the emergence and effects of topological defects and solitons in complex fluids. This review is dedicated to the memory of Marek Cieplak.
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- Award ID(s):
- 2019745
- PAR ID:
- 10513438
- Author(s) / Creator(s):
- ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; more »
- Publisher / Repository:
- Elsevier B.V.
- Date Published:
- Journal Name:
- Physics Reports
- Volume:
- 1075
- Issue:
- C
- ISSN:
- 0370-1573
- Page Range / eLocation ID:
- 1 to 137
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
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- Free Publicly Accessible Full Text
-
Accepted Manuscript
- Journal Article:
- https://doi.org/10.1016/j.physrep.2024.04.002
