Higher-order topological phases in a spring-mass model on a breathing kagome lattice

TL;DR

This paper demonstrates higher-order topological phases in a spring-mass model on a breathing kagome lattice, revealing corner states and topological properties characterized by a $rac{2 extpi}{3}$ Berry phase, with potential experimental detection.

Contribution

It introduces a mechanical model exhibiting higher-order topological phases and develops a formula for the $ ext{Z}_3$ Berry phase to characterize these phases.

Findings

Corner states appear under fixed boundary conditions.

Coupling between modes yields a $rac{2 extpi}{3}$ Berry phase.

Corner states can be experimentally detected via forced vibration.

Abstract

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.