The concept of topological energy bands and their manifestations have been demonstrated in condensed matter systems as a fantastic paradigm toward unprecedented physical phenomena and properties that are robust against disorders. Recent years, this paradigm was extended to phononic metamaterials (including mechanical and acoustic metamaterials), giving rise to the discovery of remarkable phenomena that were not observed elsewhere thanks to the extraordinary controllability and tunability of phononic metamaterials as well as versatile measuring techniques. These phenomena include, but not limited to, topological negative refraction, topological ‘sasers’ (i.e. the phononic analog of lasers), higher-order topological insulating states, non-Abelian topological phases, higher-order Weyl semimetal phases, Majorana-like modes in Dirac vortex structures and fragile topological phases with spectral flows. Here we review the developments in the field of topological phononic metamaterials from both theoretical and experimental perspectives with emphasis on the underlying physics principles. To give a broad view of topological phononics, we also discuss the synergy with non-Hermitian effects and cover topics including synthetic dimensions, artificial gauge fields, Floquet topological acoustics, bulk topological transport, topological pumping, and topological active matters as well as potential applications, materials fabrications and measurements of topological phononic metamaterials. Finally, we discuss the challenges, opportunities and future developments in this intriguing field and its potential impact on physics and materials science.

中文翻译：

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拓扑声子超材料


拓扑能带的概念及其表现形式已在凝聚态物质系统中得到证明，作为一种奇妙的范例，可以实现前所未有的物理现象和抵抗紊乱的特性。近年来，这种范式扩展到声子超材料（包括机械和声学超材料），由于声子超材料非凡的可控性和可调谐性以及多功能测量技术，发现了在其他地方未观察到的显着现象。这些现象包括但不限于拓扑负折射、拓扑“激光”（即激光的声子模拟）、高阶拓扑绝缘态、非阿贝尔拓扑相、高阶韦尔半金属相、类马约拉纳模式狄拉克涡旋结构和具有谱流的脆弱拓扑相。在这里，我们从理论和实验的角度回顾拓扑声子超材料领域的发展，重点关注基本的物理原理。为了更全面地了解拓扑声子学，我们还讨论了与非厄米效应的协同作用，涵盖的主题包括合成维度、人工规范场、Floquet 拓扑声学、体拓扑输运、拓扑泵浦和拓扑活性物质以及潜在应用、拓扑声子超材料的材料制造和测量。最后，我们讨论了这个有趣领域的挑战、机遇和未来发展及其对物理和材料科学的潜在影响。