Phonons as a platform for non-Abelian braiding and its manifestation in layered silicates

TL;DR

This paper demonstrates that multi-gap topological phonon states with non-Abelian braiding can be observed in layered silicates, with control via electric fields and strain, and signatures detectable through Raman spectroscopy.

Contribution

It introduces the first experimental platform to observe non-Abelian braiding in phonons of layered silicates, overcoming electronic constraints and enabling control of topological phase transitions.

Findings

Multi-gap topologies observed in phonon spectra of monolayer silicates.

Braiding processes can be controlled by electric field and strain.

Band inversion signatures detectable via Raman spectroscopy.

Abstract

Topological phases of matter have revolutionised the fundamental understanding of band theory and hold great promise for next-generation technologies such as low-power electronics or quantum computers. Single-gap topologies have been extensively explored, and a large number of materials have been theoretically proposed and experimentally observed. These ideas have recently been extended to multi-gap topologies with band nodes that carry non-Abelian charges, characterised by invariants that arise by the momentum space braiding of such nodes. However, the constraints placed by the Fermi-Dirac distribution to electronic systems have so far prevented the experimental observation of multi-gap topologies in real materials. Here, we show that multi-gap topologies and the accompanying phase transitions driven by braiding processes can be readily observed in the bosonic phonon spectra of known monolayer silicates. The associated braiding process can be controlled by means of an electric field and epitaxial strain, and involves, for the first time, more than three bands. Finally, we propose that the band inversion processes at the $\Gamma$ point can be tracked by following the evolution of the Raman spectrum, providing a clear signature for the experimental verification of the band inversion accompanied by the braiding process.