Phase transitions of non-Abelian charged nodal links in a spring-mass system

TL;DR

This paper demonstrates how a simple spring-mass system can realize and manipulate non-Abelian charged nodal lines, revealing topological phase transitions and linking phenomena relevant for classical phonon systems.

Contribution

It introduces a classical spring-mass model to study multi-gap topological phase transitions involving non-Abelian nodal lines, including braiding and linking processes.

Findings

Nodal lines of a three-band system are constructed in a spring-mass setup.

Braiding of nodal lines is achieved by adjusting spring constants.

Topological transitions from trivial to linked nodal lines are demonstrated.

Abstract

Although a large class of topological materials have uniformly been identified using symmetry properties of wave functions, the past two years have seen the rise of multi-gap topologies beyond this paradigm. Given recent reports of unexplored features of such phases, platforms that are readily implementable to realize them are therefore desirable. Here, we demonstrate that multi-gap topological phase transitions of non-Abelian charged nodal lines arise in classical phonon waves. By adopting a simple spring-mass system, we construct nodal lines of a three-band system. The braiding process of the nodal lines is readily performed by adjusting the spring constants. The generation and annihilation of the nodal lines are then analyzed using Euler class. Finally, we retrieve topological transitions from trivial nodal lines to a nodal link. Our work provides a simple platform that can offer diverse insights to not only theoretical but also experimental studies on multi-gap topology.