Report
Fractional defect charges in $p$-atic liquid crystals on cones
| العنوان: | Fractional defect charges in $p$-atic liquid crystals on cones |
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| المؤلفون: | Zhang, Grace H., Nelson, David R. |
| سنة النشر: | 2022 |
| المجموعة: | Condensed Matter |
| مصطلحات موضوعية: | Condensed Matter - Soft Condensed Matter |
| الوصف: | Conical surfaces, with a delta function of Gaussian curvature at the apex, are perhaps the simplest example of geometric frustration. We study two-dimensional liquid crystals with $p$-fold rotational symmetry ($p$-atics) on the surfaces of cones. For free boundary conditions at the base, we find both the ground state(s) and a discrete ladder of metastable states as a function of both the cone angle and the liquid crystal symmetry $p$. We find that these states are characterized by a set of fractional defect charges at the apex and that the ground states are in general frustrated due to effects of parallel transport along the azimuthal direction of the cone. We check our predictions for the ground state energies numerically for a set of commensurate cone angles (corresponding to a set of commensurate Gaussian curvatures concentrated at the cone apex), whose surfaces can be polygonized as a perfect triangular or square mesh, and find excellent agreement with our theoretical predictions. Comment: 20 pages, 8 figures |
| نوع الوثيقة: | Working Paper |
| URL الوصول: | http://arxiv.org/abs/2201.11201 |
| رقم الانضمام: | edsarx.2201.11201 |
| قاعدة البيانات: | arXiv |
| الوصف غير متاح. |