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Title: Topological transformations of Hopf solitons in chiral ferromagnets and liquid crystals

Abstract

Liquid crystals are widely known for their facile responses to external fields, which forms a basis of the modern information display technology. However, switching of molecular alignment field configurations typically involves topologically trivial structures, although singular line and point defects often appear as short-lived transient states. Here, we demonstrate electric and magnetic switching of nonsingular solitonic structures in chiral nematic and ferromagnetic liquid crystals. These topological soliton structures are characterized by Hopf indices, integers corresponding to the numbers of times that closed-loop-like spatial regions (dubbed “preimages”) of two different single orientations of rod-like molecules or magnetization are linked with each other. We show that both dielectric and ferromagnetic response of the studied material systems allow for stabilizing a host of topological solitons with different Hopf indices. Furthermore the field transformations during such switching are continuous when Hopf indices remain unchanged, even when involving transformations of preimages, but discontinuous otherwise.

Authors:
; ;
Publication Date:
Research Org.:
Univ. of Colorado, Boulder, CO (United States)
Sponsoring Org.:
USDOE; USDOE Office of Science (SC), Basic Energy Sciences (BES) (SC-22). Materials Sciences & Engineering Division
OSTI Identifier:
1417234
Alternate Identifier(s):
OSTI ID: 1511027
Grant/Contract Number:  
ER46921; SC0010305
Resource Type:
Published Article
Journal Name:
Proceedings of the National Academy of Sciences of the United States of America
Additional Journal Information:
Journal Name: Proceedings of the National Academy of Sciences of the United States of America Journal Volume: 115 Journal Issue: 5; Journal ID: ISSN 0027-8424
Publisher:
Proceedings of the National Academy of Sciences
Country of Publication:
United States
Language:
English
Subject:
71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS; three-dimensional soliton; self-assembly; ferromagnetism; chirality

Citation Formats

Tai, Jung-Shen B., Ackerman, Paul J., and Smalyukh, Ivan I. Topological transformations of Hopf solitons in chiral ferromagnets and liquid crystals. United States: N. p., 2018. Web. doi:10.1073/pnas.1716887115.
Tai, Jung-Shen B., Ackerman, Paul J., & Smalyukh, Ivan I. Topological transformations of Hopf solitons in chiral ferromagnets and liquid crystals. United States. doi:10.1073/pnas.1716887115.
Tai, Jung-Shen B., Ackerman, Paul J., and Smalyukh, Ivan I. Wed . "Topological transformations of Hopf solitons in chiral ferromagnets and liquid crystals". United States. doi:10.1073/pnas.1716887115.
@article{osti_1417234,
title = {Topological transformations of Hopf solitons in chiral ferromagnets and liquid crystals},
author = {Tai, Jung-Shen B. and Ackerman, Paul J. and Smalyukh, Ivan I.},
abstractNote = {Liquid crystals are widely known for their facile responses to external fields, which forms a basis of the modern information display technology. However, switching of molecular alignment field configurations typically involves topologically trivial structures, although singular line and point defects often appear as short-lived transient states. Here, we demonstrate electric and magnetic switching of nonsingular solitonic structures in chiral nematic and ferromagnetic liquid crystals. These topological soliton structures are characterized by Hopf indices, integers corresponding to the numbers of times that closed-loop-like spatial regions (dubbed “preimages”) of two different single orientations of rod-like molecules or magnetization are linked with each other. We show that both dielectric and ferromagnetic response of the studied material systems allow for stabilizing a host of topological solitons with different Hopf indices. Furthermore the field transformations during such switching are continuous when Hopf indices remain unchanged, even when involving transformations of preimages, but discontinuous otherwise.},
doi = {10.1073/pnas.1716887115},
journal = {Proceedings of the National Academy of Sciences of the United States of America},
number = 5,
volume = 115,
place = {United States},
year = {2018},
month = {1}
}

Journal Article:
Free Publicly Available Full Text
Publisher's Version of Record
DOI: 10.1073/pnas.1716887115

Citation Metrics:
Cited by: 2 works
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Figures / Tables:

Fig. 1 Fig. 1: Topological solitons. Preimages in $\mathbb{R}^3$ (and $\mathbb{S}^3$) correspond to distinct points on $\mathbb{S}^2$ form Hopf (2$^2_1$) (A) and Solomon links (4$^2_1$) (B) with linking numbers matching their Q = 1 (A) and Q = 2 (B) Hopf indices. Since the direct (ϕ) and inverse (ϕ−1) stereographic projections relatemore » smooth configurations in $\mathbb{S}^3$ and $\mathbb{R}^3$ when embedded within the uniform n0 andM0, these solitons are characterized by the $\mathbb{S}^3$ → $\mathbb{S}^2$ maps, the third homotopy group π3($\mathbb{S}^2$) = $\mathbb{Z}$ and Q ∈ $\mathbb{Z}$. Black arrows indicate circulation directions, crossing signs are marked in red color, and the colors of preimages match that of the corresponding points on $\mathbb{S}^2$.« less

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