Skyrmions in two dimensional cholesteric liquid crystals

Carlo Greco ()
Additional contact information
Carlo Greco: Polytechnic University of Bari

Partial Differential Equations and Applications, 2025, vol. 6, issue 6, 1-21

Abstract: Abstract In this paper we consider a two dimensional cholesteric liquid crystal with an applied external field, whose field configurations $$u:\mathbb {R}^2\rightarrow S^2$$ u : R 2 → S 2 are constant at infinity, and can be classified by their topological degree. We look for non trivial, topologically stable configurations (chiral skyrmions) by minimizing the Oseen-Frank energy functional over the functions u with $$\deg (u)=-1$$ deg ( u ) = - 1 . The energy functional depends on the splay ( $$K_1$$ K 1 ), twist ( $$K_2$$ K 2 ) and bend ( $$K_3$$ K 3 ) elastic constants, and, assuming that $$K_1=K_2$$ K 1 = K 2 , we show the existence of skyrmions provided the cholesteric pitch $$q_0$$ q 0 is small enough; moreover we study the compactness of such skyrmions as $$q_0\rightarrow 0$$ q 0 → 0 , and their limit. Our results generalize some previous results in the literature obtained under the assumption that $$K_1=K_2=K_3$$ K 1 = K 2 = K 3 (the well known “one-constant approximation” assumption). Moreover, in order to overcome the lack of compactness of the energy functional, we use (instead of the concentration-compactness principle) the fact that the field configurations with energy below a suitable threshold do not cover twice $$S^2$$ S 2 minus a neighborhood of the North Pole, together with a truncation argument at infinity.

Keywords: Skyrmion; Cholesteric; Minimization; Compactness; 35J50; 58E50; 76A15 (search for similar items in EconPapers)
Date: 2025
References: Add references at CitEc
Citations:

Downloads: (external link)
http://link.springer.com/10.1007/s42985-025-00348-9 Abstract (text/html)
Access to the full text of the articles in this series is restricted.

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:spr:pardea:v:6:y:2025:i:6:d:10.1007_s42985-025-00348-9

Ordering information: This journal article can be ordered from
https://www.springer.com/journal/42985/

DOI: 10.1007/s42985-025-00348-9

Access Statistics for this article

Partial Differential Equations and Applications is currently edited by Zhitao Zhang

More articles in Partial Differential Equations and Applications from Springer
Bibliographic data for series maintained by Sonal Shukla () and Springer Nature Abstracting and Indexing ().