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  • Open Access

Quantized non-Abelian helicity of flat bands in 2D Floquet topological photonic insulators

Bo Leng and Vien Van*

  • Department of Electrical and Computer Engineering, University of Alberta, Edmonton, Alberta, Canada T6G 2V4

  • *Contact author: vien@ualberta.ca
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Phys. Rev. Research 8, 023104 – Published 1 May, 2026

DOI: https://doi.org/10.1103/3flt-3gv6

Abstract

Flat-band states in topological systems provide a unique platform for investigating strongly correlated phenomena and many-body physics. However, in two-dimensional (2D) static tight-binding systems, perfectly flat bands can only exist in the topologically trivial phase, as characterized by a zero Chern number. Here, we show that by introducing periodic driving into a 2D photonic Lieb lattice composed of coupled microring resonators, the resulting Floquet topological insulator can host perfectly flat bands with nontrivial topology. In particular, by tracking the evolution of the flat-band modes over each cycle, we show that the non-Abelian displacements of the flat-band modes are characterized by a nontrivial quantized helicity even though the quasienergy bands have zero Chern number. The helical motion of the flat-band modes can be described by a braiding of the world lines of their trajectories, with a nontrivial winding number directly connected to the helicity. We also propose a scheme to experimentally measure the quantized non-Abelian helicity in a microring lattice subject to a synthetic magnetic field. These results suggest that Floquet topological photonic insulators based on coupled microring resonators can provide a versatile platform for investigating non-Abelian topological physics and strongly correlated phenomena in photonic flat-band systems.

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Phys. Rev. Research 8, 023104– Published 1 May, 2026
  • Received 31 January 2026
  • Accepted 7 April 2026
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Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article's title, journal citation, and DOI.

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