Ground States of Crystalline Caps: Generalized Jellium on Curved Space

Abstract

We study the structure and elastic energy of the ground states of crystalline caps conforming to a spherical surface. These ground states consist of positive disclination defects in structures spanning from flat and weakly curved crystals to closed shells. We compare two different continuum theories and one discrete-lattice approach for the elastic energy of defective caps. We first investigate the transition between defect-free caps to single-disclination ground states and show that it is characterized by continuous symmetry-breaking transition. Further, we show that ground states with icosahedral subgroup symmetries in caps arise across a range of curvatures, even far from the closure point of complete shells. Thus, while superficially similar to other models of 2D `jellium' (e.g. superconducting disks and 2D Wigner crystals), the interplay between the free edge of crystalline caps and the non-Euclidean geometry of its embedding leads to non trivial ground state behaviors, without counterpart in planar jellium models.

arXiv commentMain text: 6 pages, 3 figures; Supplemental Information: 9 pages, 8 figures, 1 table (replaced version corrects author listing)

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• Stress accumulation versus shape flattening in frustrated, warped-jigsaw particle assemblies
• Exact Solution for Elastic Networks on Curved Surfaces
• Defects in Conformal Crystals: Discrete vs. Continuous Disclination Models
• A simple, general criterion for onset of disclination disorder on curved surfaces
• Geometry and physics in the deformations of crystalline caps
• Predicting the Characteristics of Defect Transitions on Curved Surfaces
• General Solution for Elastic Networks on Arbitrary Curved Surfaces in the Absence of Rotational Symmetry