Defect Organization in Coexisting Hexagonal and Square Lattices on Ellipsoids
Abstract
Curvature and topology jointly organize defects in two-dimensional crystals, but their combined role remains unresolved when competing lattice symmetries coexist with spatially varying curvature. We use simulated-annealing Langevin dynamics to study Hertzian particles forming coexisting hexagonal (Hex) and square (Sq) lattices on prolate and oblate ellipsoids. Mapping reduced density and aspect ratio reveals a broad sequence of scar and domain-based morphologies in both Hex-dominant and Sq-dominant backgrounds. Latitude-resolved comparisons show that Gaussian curvature biases defects toward its maxima under weak deformation. Strong prolateness, however, confines high curvature to small polar caps that cannot independently accommodate all defect motifs. Defects then spread toward lower-curvature latitudes to relieve defect crowding and elastic repulsion. In the Hex-dominant regime, this competition drives vertex-contacted domains with neutralized corner contacts, and compensating positive defects locate away from the poles. The Sq-dominant regime features Hex-rich triangular domains, bridged states, and linear or open scars similarly reorganized by curvature anisotropy. On oblate ellipsoids, the extended equatorial high-curvature belt allows defects to separate azimuthally while remaining curvature-localized. This work elucidates that nonuniform curvature can engineer rich defect patterns by selecting the spatial distribution of topological charge and the connectivity of finite defect motifs.
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BibTeX
@misc{liu2026defect,
title = {{Defect Organization in Coexisting Hexagonal and Square Lattices on Ellipsoids}},
author = {Wenyu Liu and Han Xie and Baohui Li and Jeff Z. Y. Chen and Yao Li},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.37668},
eprint = {2609.37668},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.37668},
note = {CC BY-NC-ND 4.0},
}
RIS
TY - UNPB
TI - Defect Organization in Coexisting Hexagonal and Square Lattices on Ellipsoids
AU - Wenyu Liu
AU - Han Xie
AU - Baohui Li
AU - Jeff Z. Y. Chen
AU - Yao Li
PY - 2026
DA - 2026/09/29
PB - arXiv
DO - 10.48550/arxiv.2609.37668
UR - https://arxiv.org/abs/2609.37668
AB - Curvature and topology jointly organize defects in two-dimensional crystals, but their combined role remains unresolved when competing lattice symmetries coexist with spatially varying curvature. We use simulated-annealing Langevin dynamics to study Hertzian particles forming coexisting hexagonal (Hex) and square (Sq) lattices on prolate and oblate ellipsoids. Mapping reduced density and aspect ratio reveals a broad sequence of scar and domain-based morphologies in both Hex-dominant and Sq-dominant backgrounds. Latitude-resolved comparisons show that Gaussian curvature biases defects toward its maxima under weak deformation. Strong prolateness, however, confines high curvature to small polar caps that cannot independently accommodate all defect motifs. Defects then spread toward lower-curvature latitudes to relieve defect crowding and elastic repulsion. In the Hex-dominant regime, this competition drives vertex-contacted domains with neutralized corner contacts, and compensating positive defects locate away from the poles. The Sq-dominant regime features Hex-rich triangular domains, bridged states, and linear or open scars similarly reorganized by curvature anisotropy. On oblate ellipsoids, the extended equatorial high-curvature belt allows defects to separate azimuthally while remaining curvature-localized. This work elucidates that nonuniform curvature can engineer rich defect patterns by selecting the spatial distribution of topological charge and the connectivity of finite defect motifs.
ER -