Department of Mathematics, Massachusetts Institute of Technology, 77 Massachusetts Avenue, Cambridge, MA 02139-4307, USA.
Soft Matter. 2018 Mar 28;14(12):2329-2338. doi: 10.1039/c7sm02233f. Epub 2018 Feb 28.
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.
拓扑缺陷塑造了物理系统的物质和输运性质。从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，到早期宇宙中形成的畴结构，都有例子。Kibble-Zurek (KZ) 机制描述了具有恒定有限淬火速率的连续非平衡相变中的拓扑缺陷形成。对于平面欧几里得几何中的二阶相变，已经通过实验和数值验证了普遍的 KZ 标度定律，但它们在弯曲和拓扑非平凡系统中的非热相变中的有效性仍然存在问题。在这里，我们使用最近经过实验证实的理论来研究通过应力淬火双层材料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 型幂律。此外，成核序列与球形胶体晶体的最近实验观察结果一致。我们的结果表明，弯曲弹性双层为研究非平面几何中非热相变的普遍性质提供了一个可实验访问的宏观系统。
