Quantized non-Abelian helicity of flat bands in 2D Floquet topological photonic insulators
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arXiv
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| Format: | Preprint |
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2026
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| _version_ | 1866914283265196032 |
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| author | Leng, Bo Van, Vien |
| author_facet | Leng, Bo Van, Vien |
| contents | Flat-band states in topological systems provide a unique platform for investigating strongly correlated phenomena and many body physics. However, in 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 quasi-energy 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2601_19028 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Quantized non-Abelian helicity of flat bands in 2D Floquet topological photonic insulators Leng, Bo Van, Vien Optics Flat-band states in topological systems provide a unique platform for investigating strongly correlated phenomena and many body physics. However, in 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 quasi-energy 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. |
| title | Quantized non-Abelian helicity of flat bands in 2D Floquet topological photonic insulators |
| topic | Optics |
| url | https://arxiv.org/abs/2601.19028 |