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Umbilic lines in orientational order
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Machon, Thomas and Alexander, Gareth P. (2016) Umbilic lines in orientational order. Physical Review X, 6 (1). pp. 1-19. 011033. doi:10.1103/PhysRevX.6.011033 ISSN 2160-3308.
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Official URL: http://dx.doi.org/10.1103/PhysRevX.6.011033
Abstract
Three-dimensional orientational order in systems whose ground states possess nonzero gradients typically exhibits linelike structures or defects: λ lines in cholesterics or Skyrmion tubes in ferromagnets, for example. Here, we show that such lines can be identified as a set of natural geometric singularities in a unit vector field, the generalization of the umbilic points of a surface. We characterize these lines in terms of the natural vector bundles that the order defines and show that they give a way to localize and identify Skyrmion distortions in chiral materials—in particular, that they supply a natural representative of the Poincaré dual of the cocycle describing the topology. Their global structure leads to the definition of a self-linking number and helicity integral which relates the linking of umbilic lines to the Hopf invariant of the texture.
Item Type: | Journal Article | ||||||||
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Subjects: | Q Science > QC Physics | ||||||||
Divisions: | Faculty of Science, Engineering and Medicine > Science > Physics | ||||||||
Library of Congress Subject Headings (LCSH): | Condensed matter | ||||||||
Journal or Publication Title: | Physical Review X | ||||||||
Publisher: | American Physical Society | ||||||||
ISSN: | 2160-3308 | ||||||||
Official Date: | 28 March 2016 | ||||||||
Dates: |
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Volume: | 6 | ||||||||
Number: | 1 | ||||||||
Number of Pages: | 19 | ||||||||
Page Range: | pp. 1-19 | ||||||||
Article Number: | 011033 | ||||||||
DOI: | 10.1103/PhysRevX.6.011033 | ||||||||
Status: | Peer Reviewed | ||||||||
Publication Status: | Published | ||||||||
Access rights to Published version: | Open Access (Creative Commons) | ||||||||
Date of first compliant deposit: | 4 April 2016 | ||||||||
Date of first compliant Open Access: | 4 April 2016 | ||||||||
Funder: | Engineering and Physical Sciences Research Council (EPSRC), University of Warwick Vice Chancellor Scholarship, University of Warwick. Institute of Advanced Study (IAS) | ||||||||
Grant number: | A.MACX.0002 (EPSRC), EP/N007883/1 (EPSRC) |
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