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

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.

arXiv comment18 pages, 12 figures

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• Three-dimensional $\mathcal{P}\mathcal{T}$-symmetric topological phases with Pontryagin index
• Experimental demonstration of non-adjacent band topology connecting multiple nodal links
• Disorder-induced topological quantum phase transitions in multi-gap Euler semimetals
• Projected spin texture as a bulk indicator of fragile topology
• Andreev reflection in Euler materials
• Observing the nodal-line conversion determined by the relative homotopy
• Berry curvature inside parity-time-symmetry protected exceptional surface
• Floquet non-Abelian topological charges and edge states
• Euler band topology in superfluids and superconductors
• Three-dimensional spinless Euler insulators with rotational symmetry