Generating the Hopf Fibration Experimentally in Nematic Liquid Crystals

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Generating the Hopf Fibration Experimentally in Nematic Liquid Crystals

Bryan Gin-ge Chen, Paul J. Ackerman, Gareth P. Alexander, Randall D. Kamien, and Ivan I. Smalyukh

Phys. Rev. Lett. 110, 237801 – Published 3 June 2013

See Viewpoint: Topology with Liquid Crystals

Abstract

The Hopf fibration is an example of a texture: a topologically stable, smooth, global configuration of a field. Here we demonstrate the controlled sculpting of the Hopf fibration in nematic liquid crystals through the control of point defects. We demonstrate how these are related to torons by use of a topological visualization technique derived from the Pontryagin-Thom construction.

Received 30 December 2012

DOI:https://doi.org/10.1103/PhysRevLett.110.237801

Viewpoint

Topology with Liquid Crystals

Published 3 June 2013

Molecules in a liquid crystal order into a pattern whose links and twists resemble a Hopf fibration, a geometric shape from topology with unusual properties.

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Authors & Affiliations

Bryan Gin-ge Chen^1,2, Paul J. Ackerman³, Gareth P. Alexander⁴, Randall D. Kamien², and Ivan I. Smalyukh³

¹Instituut-Lorentz, Universiteit Leiden, Postbus 9506, 2300 RA Leiden, Netherlands
²Department of Physics and Astronomy, University of Pennsylvania, Philadelphia, Pennsylvania 19104, USA
³Department of Physics, University of Colorado, Boulder, Colorado 80309, USA
⁴Department of Physics and Centre for Complexity Science, University of Warwick, Coventry CV4 7AL, United Kingdom