方向相关手性与手征设计
Orientation-dependent handedness and chiral design
摘要：
手征性在从生物自组装到光学超材料设计的各个领域都占据着核心地位。开尔文勋爵给出的手征性定义将手征性与镜像对称性的缺乏联系在一起：无法将物体叠加在其镜像上。虽然这个定义指导了一个多世纪的手征物体的分类，但基于这个定义的手征现象的量化已经被证明是难以捉摸的，如果不是不可能的话，就像手征连通性悖论所表现的那样。在这项工作中，我们提出了一个量化方案，在该方案中，一个对象的手性取决于它被视为方向。虽然与熟悉的手征概念（如右手定则）一致，但这个框架允许物体同时是右手和左手的。我们证明了这种取向的依赖性在三个不同的系统-仿生弹性双层，手性螺旋桨，光学超材料-并找到定量协议与手性pseudotensors的形式，我们明确计算。这种方法的使用解决了现有的悖论，并自然地使设计的手的超材料的对称性原则。
英文摘要：
Chirality occupies a central role in fields ranging from biological self-assembly to the design of optical metamaterials. The definition of chirality, as given by Lord Kelvin, associates chirality with the lack of mirror symmetry: the inability to superpose an object on its mirror image. While this definition has guided the classification of chiral objects for over a century, the quantification of handed phenomena based on this definition has proven elusive, if not impossible, as manifest in the paradox of chiral connectedness. In this work, we put forward a quantification scheme in which the handedness of an object depends on the direction in which it is viewed. While consistent with familiar chiral notions, such as the right-hand rule, this framework allows objects to be simultaneously right and left handed. We demonstrate this orientation dependence in three different systems - a biomimetic elastic bilayer, a chiral propeller, and optical metamaterial - and find quantitative agreement with chirality pseudotensors whose form we explicitly compute. The use of this approach resolves the existing paradoxes and naturally enables the design of handed metamaterials from symmetry principles.
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