Comment on "Floquet non-Abelian topological insulator and multifold bulk-edge correspondence"

TL;DR

This paper critically examines a recent study on Floquet non-Abelian topological insulators, highlighting that the original claims lack sufficient proof for total bulk characterization and are not as novel as suggested.

Contribution

The authors provide a critical commentary clarifying that the original work's claims about multi-gap topology and bulk-edge correspondence are not fully supported and are not entirely new.

Findings

Original claims lack rigorous proof for bulk characterization.

Rephrasing of existing Zak phase descriptions.

Contrasts with earlier work on Floquet phases and Dirac strings.

Abstract

We comment on the recent paper ``Floquet non-Abelian topological insulator and multifold bulk-edge correspondence" by Tianyu Li and Haiping Hu, Nat. Comm. {\bf 14}, 6418 (2023). Apart from the fact that the authors unjustly imply to study multi-gap topology in Floquet systems for the first time, only known homotopic relations are presented. While such insights are used to present interesting Floquet phenomena and phases, which is an attractive result in itself, they cannot be used to deduce the total bulk characterization in the dynamical context without further proof. In fact, the authors essentially rephrase a Zak phase description. These results should in particular be contrasted to earlier results, arXiv:2208.12824, in which static-compatible Zak phases {\it and} dynamical Dirac strings were shown to be able to {\it distinguish} rather similar non-Abelian Floquet phases in $2+1$ dimensional systems. As a result, the claim of a sharp multifold bulk-edge correspondence cannot be concluded from the given arguments.