We propose a realization of higher-order topological phases in a spring-mass model with a breathing kagome structure. To demonstrate the existence of the higher-order topological phases, we characterize the topological properties and show that the corner states appear under the fixed boundary condition. To characterize the topological properties, we introduce a formula for the ${\mathbb{Z}}_3$ Berry phases in the Brillouin zone. From the numerical result of this ${\mathbb{Z}}_3$ Berry phase, we have elucidated that coupling between the longitudinal and transverse modes yields a state characterized by the Berry phase $\frac{2\pi }{3}$ for our mechanical breathing kagome model. In addition, we suggest that the corner states can be detected experimentally through a forced vibration.

中文翻译：

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呼吸孔戈梅晶格上的弹簧质量模型中的高阶拓扑相

我们建议在具有呼吸kagome结构的弹簧质量模型中实现高阶拓扑阶段。为了说明高阶拓扑相的存在，我们表征了拓扑性质，并表明角状态在固定边界条件下出现。为了表征拓扑特性，我们引入了一个公式${\mathbb{ž}}_3$浆果阶段在布里渊区。从这个数值结果${\mathbb{ž}}_3$ 贝里相，我们已经阐明了纵向和横向模态之间的耦合会产生一个以贝里相为特征的状态 $\frac{2\pi }{3}$用于我们的机械呼吸kagome模型。此外，我们建议可以通过强制振动来实验检测转角状态。