Real-space origin of topological band gaps, localization, and reentrant phase transitions in gyroscopic metamaterials
Real-space origin of topological band gaps, localization, and reentrant phase transitions in gyroscopic metamaterials
复制标题
陀螺超材料中拓扑带隙、局部化和重入相变的实空间起源
DOI：
10.1103/physreve.104.025007
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发表时间：
2021
影响因子：
2.4
通讯作者：
Irvine, William T.
中科院分区：
文献类型：
--
作者：
Mitchell, Noah P.;Turner, Ari M.;Irvine, William T.
相互作用陀螺仪的晶格自然支持带隙和拓扑保护波沿材料边界传输。最近，作者和他们的合作者发现这种耦合陀螺仪的无定形排列也支持非平凡拓扑相。与周期系统相比，对于带隙和带拓扑有一个全面的理解和预测框架，非晶材料的谱隙和拓扑理论仍然不太发达。在这里，我们使用实验、数值和分析工具来解决局部相互作用和非平凡拓扑之间的关系。我们从辛力学框架内的运动方程的推导开始。然后，我们提出了一种预测间隙是否存在和仅使用网络的局部特征近似陈数的一般方法，绕过了系统动态矩阵的昂贵对角化。最后，我们研究了陀螺超材料中强无序与带拓扑的相互作用，并发现非晶陀螺陈氏绝缘子表现出与周期晶格相似的临界行为。我们的实验和模拟还揭示了拓扑安德森绝缘转变，其中无序将一个平凡的相驱动到拓扑相。
Lattices of interacting gyroscopes naturally support band gaps and topologically protected wave transport along material boundaries. Recently the authors and their collaborators found that amorphous arrangements of such coupled gyroscopes also support nontrivial topological phases. In contrast to periodic systems, for which there is a comprehensive understanding and predictive framework for band gaps and band topology, the theory of spectral gaps and topology for amorphous materials remains less developed. Here we use experiments, numerics, and analytic tools to address the relationship between local interactions and nontrivial topology. We begin with a derivation of the equations of motion within the framework of symplectic mechanics. We then present a general method for predicting whether a gap exists and for approximating the Chern number using only local features of a network, bypassing the costly diagonalization of the system's dynamical matrix. Finally we study how strong disorder interacts with band topology in gyroscopic metamaterials and find that amorphous gyroscopic Chern insulators exhibit similar critical behavior to periodic lattices. Our experiments and simulations additionally reveal a topological Anderson insulation transition, wherein disorder drives a trivial phase into a topological one.