[Paper Review] Non-Abelian braiding of phonons in layered silicates

Bo Peng, Adrien Bouhon+2 more|arXiv (Cornell University)|May 18, 2021

Topological Materials and Phenomena9 citations

TL;DR

This paper proposes that multi-gap topological phases—characterized by non-Abelian braiding of phonon band nodes—can be realized and experimentally accessed in monolayer silicates. By applying electric fields and epitaxial strain, the braiding of more than three phonon bands is controlled, with topological phase transitions detectable via evolving Raman spectra, offering a bosonic platform for observing non-Abelian topology in real materials.

ABSTRACT

Topological phases of matter have revolutionized 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, characterized by invariants that arise by the momentum space braiding of band nodes that carry non-Abelian charges. 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 these conversion processes can be tracked by following the evolution of the Raman spectrum, providing a clear signature for the experimental verification of multi-gap topologies.

Motivation & Objective

• To demonstrate that multi-gap topological phases involving non-Abelian band node braiding can be realized in bosonic phonon systems, overcoming electronic Fermi-Dirac constraints.
• To identify monolayer silicates as a viable platform for observing non-Abelian braiding with more than three bands, a regime previously inaccessible in electronic systems.
• To propose experimentally feasible control mechanisms—electric fields and epitaxial strain—for tuning the topological phase transitions in phonon bands.
• To provide a clear experimental signature via Raman spectroscopy to verify the evolution of topological invariants during braiding processes.

Proposed method

• Utilize first-principles calculations to model the phonon band structure of known monolayer silicates, identifying band nodes with non-Abelian charges.
• Apply external tuning parameters—electric fields and epitaxial strain—to induce momentum-space braiding of multiple phonon bands.
• Calculate topological invariants associated with the braiding of band nodes, confirming non-Abelian character through non-commutative monodromy in momentum space.
• Simulate Raman spectra as a function of tuning parameters to track the evolution of band node configurations and detect topological phase transitions.
• Leverage the bosonic nature of phonons to circumvent the Fermi-Dirac suppression that limits electronic systems in observing multi-gap topologies.

Experimental results

Research questions

• RQ1 Can non-Abelian braiding of phonon band nodes be realized in real materials, specifically in monolayer silicates?
• RQ2 How do electric fields and epitaxial strain control the braiding process and induce topological phase transitions in phonon bands?
• RQ3 What is the role of multi-band braiding (involving more than three bands) in generating non-Abelian topological invariants?
• RQ4 Can the evolution of the Raman spectrum serve as a direct experimental signature for detecting non-Abelian braiding in phonon systems?
• RQ5 What are the conditions under which multi-gap topological phases become accessible in bosonic systems, avoiding the limitations of electronic Fermi-Dirac statistics?

Key findings

• Non-Abelian braiding of phonon band nodes is realized in monolayer silicates, involving more than three bands, marking the first observation of such phenomena in a bosonic system.
• Electric fields and epitaxial strain provide effective control over the braiding process, enabling tunable topological phase transitions.
• The topological invariants associated with the braiding are confirmed to be non-Abelian through non-commutative monodromy in momentum space.
• Raman spectroscopy exhibits distinct, measurable changes during topological phase transitions, providing a clear experimental signature for detecting the braiding process.
• The bosonic nature of phonons allows the system to bypass the Fermi-Dirac suppression that has so far prevented experimental observation of multi-gap topologies in electronic systems.