微形态超材料的拓扑力学
Topological Mechanics of Micromorphic Metamaterials
摘要：
拓扑力学是沟通量子物理、牛顿物理与材料力学之间的桥梁。它要求材料的离散模型与量子物质的拓扑特征相似。尽管使用物质的连续模型来弥合这一差距似乎具有挑战性，但我们在这里证明了这种可能性。本文基于微观形态理论，通过对超材料拓扑力学的研究，证明了量子连续介质力学缺口的弥合。建立了一种通用的超材料微观模型，并用于研究其拓扑特性。定义了带隙、带局域化和带反转的条件。虽然闭合拓扑绝缘体的带隙显然是由于能带局域化，我们证明了一种机制，关闭带隙没有带局域化。此外，尽管事实上，许多拓扑绝缘体的带反转不能完成没有关闭的间隙，我们展示了一个光学带反转的情况下，没有间隙关闭。我们可以预见，这里探讨的超材料的特殊拓扑特性将有助于先进的拓扑绝缘体的设计，并打开新的场地的拓扑绝缘体的机械应用的实施。
英文摘要：
The topological mechanics is a perfect tool that can bridge the gap between the quantum and Newtonian physics and mechanics of materials. It requires discrete models of the material with analogies with the topological characteristics of quantum matter. Despite bridging this gap using continuous models of matter would seem challenging, we demonstrate here this possibility. We demonstrate the bridging of the quantum-continuum mechanics gap by studying the topological mechanics of metamaterials based on the micromorphic theory. A general micromorphic model of metamaterials is developed and used to study their topological characteristics. The conditions of the band-gaps, band localization, and band inversion are defined. Whereas closing the band-gap of topological insulator is obviously due to band localization, we demonstrate a mechanism of closing the band-gap with no band localization. In addition, despite the fact that the band inversion of many topological insulators cannot be completed without closing the gap, we demonstrate a case of optical band inversion with no gap closing. We foresee that the exceptional topological characteristics of metamaterials explored here will help in the design of advanced topological insulators, and open new venues of the implementations of topological insulators in mechanical applications.
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