Annual Review of Condensed Matter Physics ( IF 22.6 ) Pub Date : 2018-03-12 00:00:00 , DOI: 10.1146/annurev-conmatphys-033117-054235 Xiaoming Mao 1 , Tom C. Lubensky 2
This is a review on the emergent field of topological mechanics, where concepts from electronic topological states of matter are applied to mechanics. We focus on the subcategory of topological mechanics of Maxwell lattices, which are mechanical frames having average coordination numbers equal to twice their spatial dimension, 〈z〉=2d, leaving them on the verge of mechanical instability. We start by introducing examples of Maxwell lattices, describing their elastic properties, and discussing their general classification. We then focus on topological phonon modes of these lattices by reviewing recent theoretical progress on one-dimensional chains and two-dimensional lattices that exhibit topologically protected zero-frequency phonon modes on edges and domain walls. We also propose metamaterials based on Maxwell lattices with unusual topologically protected mechanical properties.
中文翻译:
麦克斯韦格和拓扑力学
这是对拓扑力学的新兴领域的回顾,该领域将物质的电子拓扑状态的概念应用于力学。我们关注麦克斯韦格的拓扑力学子类别,它们是平均坐标数等于其空间尺寸两倍的机械框架,〈z〉 = 2 d,使它们处于机械不稳定的边缘。我们从介绍麦克斯韦格的例子开始,描述它们的弹性,并讨论它们的一般分类。然后,我们通过回顾一维链和二维晶格的最新理论进展来关注这些晶格的拓扑声子模,这些一维链和二维晶格在边缘和畴壁上显示出拓扑受保护的零频声子模。我们还提出了基于麦克斯韦晶格的超常材料,具有异常的拓扑保护机械性能。