ArticleProceedings of the National Academy of Sciences of the United States of America2015
Knot theory realizations in nematic colloids.
Article in Proceedings of the National Academy of Sciences of the United States of America, 2015. The graph could read no effect estimate from its abstract, so it casts no vote on the map. Cited by 12 papers.
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Who cites it
12 citing papers in PubMed.
- Reconfigurable non-Abelian braiding of nematic bits.Nature materials · 2026Article
- Activity drives self-assembly of passive soft inclusions in active nematics.Nature communications · 2026Article
- Fabrication of Chiral Liquid Crystal Pinwheel Arrays Through Capillarity-Assisted Particle Assembly.Small (Weinheim an der Bergstrasse, Germany) · 2025Article
- Moiré effect enables versatile design of topological defects in nematic liquid crystals.Nature communications · 2024Article
- Continuous generation of topological defects in a passively driven nematic liquid crystal.Nature communications · 2022Article
- Topological braiding and virtual particles on the cell membrane.Proceedings of the National Academy of Sciences of the United States of America · 2021Article
- Degenerate conic anchoring and colloidal elastic dipole-hexadecapole transformations.Nature communications · 2019Article
- Nematic Liquid-Crystal Colloids.Materials (Basel, Switzerland) · 2017Review
- Bipolar configuration with twisted loop defect in chiral nematic droplets under homeotropic surface anchoring.Scientific reports · 2017Article
- Lattice topology dictates photon statistics.Scientific reports · 2017Article
- Global defect topology in nematic liquid crystals.Proceedings. Mathematical, physical, and engineering sciences · 2016Article
- Creation and manipulation of topological states in chiral nematic microspheres.Nature communications · 2015Article
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Authors and funding
4 authors.
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Abstract
Nematic braids are reconfigurable knots and links formed by the disclination loops that entangle colloidal particles dispersed in a nematic liquid crystal. We focus on entangled nematic disclinations in thin twisted nematic layers stabilized by 2D arrays of colloidal particles that can be controlled with laser tweezers. We take the experimentally assembled structures and demonstrate the correspondence of the knot invariants, constructed graphs, and surfaces associated with the disclination loop to the physically observable features specific to the geometry at hand. The nematic nature of the medium adds additional topological parameters to the conventional results of knot theory, which couple with the knot topology and introduce order into the phase diagram of possible structures. The crystalline order allows the simplified construction of the Jones polynomial and medial graphs, and the steps in the construction algorithm are mirrored in the physics of liquid crystals.
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