Topological defects shape the material and transport properties of physical systems. Examples range from vortex lines in quantum superfluids, defect-mediated buckling of graphene, and grain boundaries in ferromagnets and colloidal crystals, to domain structures formed in the early universe. The Kibble–Zurek (KZ) mechanism describes the topological defect formation in continuous non-equilibrium phase transitions with a constant finite quench rate. Universal KZ scaling laws have been verified experimentally and numerically for second-order transitions in planar Euclidean geometries, but their validity for non-thermal transitions in curved and topologically nontrivial systems still poses open questions. Here, we use recent experimentally confirmed theory to investigate topological defect formation in curved elastic surface crystals formed by stress-quenching a bilayer material. For both spherical and toroidal crystals, we find that the defect densities follow KZ-type power laws. Moreover, the nucleation sequences agree with recent experimental observations for spherical colloidal crystals. Our results suggest that curved elastic bilayers provide an experimentally accessible macroscopic system to study universal properties of non-thermal phase transitions in non-planar geometries.

中文翻译：

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弯曲的弹性表面晶体中的缺陷形成动力学†

拓扑缺陷决定了物理系统的材料和传输特性。示例包括量子超流体中的涡旋线，石墨烯的缺陷介导的屈曲，铁磁体和胶体晶体中的晶界以及在早期宇宙中形成的畴结构。Kibble-Zurek（KZ）机制描述了在连续的非平衡相变中以恒定的有限淬灭速率形成的拓扑缺陷。对于平面欧几里得几何中的二阶跃迁，已经通过实验和数值方法验证了通用KZ缩放定律，但是它们对于弯曲和拓扑非平凡系统中的非热跃迁的有效性仍然存在未解决的问题。这里，我们使用最新的实验证实的理论来研究通过应力淬火双层材料而形成的弯曲弹性表面晶体中的拓扑缺陷形成。对于球形和环形晶体，我们发现缺陷密度遵循KZ型幂定律。而且，成核序列与球形胶体晶体的最新实验观察结果一致。我们的结果表明，弯曲的弹性双层膜提供了一个实验可访问的宏观系统，以研究非平面几何形状中非热相变的普遍性质。