Helical edge states and topological phase transitions in phononic systems using bi-layered lattices

TL;DR

This paper introduces a method to create topologically protected helical edge states in phononic lattices using bi-layered structures, demonstrating tunable topological phase transitions with passive mechanical components.

Contribution

It develops a systematic approach to transform quantum edge state lattices into phononic systems and demonstrates topological phase tunability in passive mechanical lattices.

Findings

Edge states are realized in phononic bi-layered lattices.

Topological phase transitions are achieved by varying spring stiffness.

Robustness of edge states to mechanical imperfections is shown.

Abstract

We propose a framework to realize helical edge states in phononic systems using two identical lattices with interlayer couplings between them. A methodology is presented to systematically transform a quantum mechanical lattice which exhibits edge states to a phononic lattice, thereby developing a family of lattices with edge states. Parameter spaces with topological phase boundaries in the vicinity of the transformed system are illustrated to demonstrate the robustness to mechanical imperfections. A potential realization in terms of fundamental mechanical building blocks is presented for the hexagonal and Lieb lattices. The lattices are composed of passive components and the building blocks are a set of disks and linear springs. Furthermore, by varying the spring stiffness, topological phase transitions are observed, illustrating the potential for tunability of our lattices.