Umbilic Lines in Orientational Order

作者：Machon Thomas; Alexander Gareth P

来源：Physical Review X, 2016, 6(1): 011033.

DOI：10.1103/PhysRevX.6.011033

• Condensed Matter Physics
• Interdisciplinary Physics
• Soft Matter

Three-dimensional orientational order in systems whose ground states possess nonzero gradients typically exhibits linelike structures or defects:. 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 Poincare 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.

• 出版日期2016-3-28