Contact Topology and the Classification of Disclination Lines in Cholesteric Liquid Crystals

Pollard, Joseph; Alexander, Gareth P.

Abstract

We give a complete topological classification of defect lines in cholesteric liquid crystals using methods from contact topology. By focusing on the role played by the chirality of the material, we demonstrate a fundamental distinction between “tight” and “overtwisted” disclination lines not detected by standard homotopy theory arguments. The classification of overtwisted lines is the same as nematics, however, we show that tight disclinations possess a topological layer number that is conserved as long as the twist is nonvanishing. Finally, we observe that chirality frustrates the escape of removable defect lines, and explain how this frustration underlies the formation of several structures observed in experiments.

Citation

Pollard, J., & Alexander, G. P. (2023). Contact Topology and the Classification of Disclination Lines in Cholesteric Liquid Crystals. Physical Review Letters, 130(22), Article 228102. https://doi.org/10.1103/physrevlett.130.228102

• Journal Article Type: Article
• Acceptance Date: May 16, 2023
• Online Publication Date: Jun 1, 2023
• Publication Date: Jun 2, 2023
• Deposit Date: Sep 18, 2023
• Publicly Available Date: Sep 18, 2023
• Journal: Physical Review Letters
• Print ISSN: 0031-9007
• Electronic ISSN: 1079-7114
• Publisher: American Physical Society
• Peer Reviewed: Peer Reviewed
• Volume: 130
• Issue: 22
• Article Number: 228102
• DOI: https://doi.org/10.1103/physrevlett.130.228102
• Public URL: https://durham-repository.worktribe.com/output/1741312