Elastic quantum spin-Hall effect in Kagome lattices

TL;DR

This paper demonstrates the realization of a quantum spin-Hall insulator in a Kagome lattice using a mass-spring system, showing topological edge states with robust, scatterless propagation around corners.

Contribution

It introduces a mechanical analog of QSHI in a Kagome lattice and analyzes topological transitions using numerical and analytical methods.

Findings

Topological edge states are identified in the Kagome lattice.

Edge states exhibit scatterless propagation around sharp corners.

The topological transition is characterized by a Chern number variation.

Abstract

A Quantum Spin-Hall Insulator (QSHI) is implemented into a simple mass-spring Kagome lattice. The transition from the trivial state to the topological one is described by an invariant Chern number function of a contrast parameter. The band diagram and helical edge states characteristic of QSHI are obtained by a combination of numerical and analytical methods. In particular, these states are shown to be Stoneley wave solutions to a set of asymptotic continuous motion equations. Last, scatterless propagation of polarized topological edge waves around sharp corners is demonstrated and robustness is assessed through a parametric study.