Singular flat bands in three dimensions: Landau level spreading, quantum geometry, and Weyl reconstruction
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arXiv
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| Autori principali: | , , |
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| Natura: | Preprint |
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2025
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| author | Kawakami, Takuto Igarashi, Yuji Koshino, Mikito |
| author_facet | Kawakami, Takuto Igarashi, Yuji Koshino, Mikito |
| contents | We theoretically investigate three-dimensional singular flat band systems, focusing on their quantum geometric properties and response to external magnetic fields. As a representative example, we study the pyrochlore lattice, which hosts a pair of degenerate flat bands touching a dispersive band. We derive a three-orbital effective continuum model that captures the essential features near the band-touching point. Within this framework, we identify the point-like topological singularity on a planar manifold defined by the degenerate flat band eigenvectors. This singularity strongly influences the quantum geometry and results in a characteristic Landau level structure, where the levels spread over a finite energy range. We show that this structure reflects the underlying band reconstruction due to the orbital Zeeman effect, which lifts the flat band degeneracy and induces the Weyl-semimetal-like dispersion near the singularity. Our analysis reveals that the range of Landau level spreading is proportional to the quantum metric of each Zeeman-split band. We further demonstrate that adding a small dispersion via longer-range . Finally, we show that our approach extends naturally to systems with higher orbital angular momentum, indicating the robustness of these features in a broad class of three-dimensional flat band models. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2506_14154 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Singular flat bands in three dimensions: Landau level spreading, quantum geometry, and Weyl reconstruction Kawakami, Takuto Igarashi, Yuji Koshino, Mikito Mesoscale and Nanoscale Physics We theoretically investigate three-dimensional singular flat band systems, focusing on their quantum geometric properties and response to external magnetic fields. As a representative example, we study the pyrochlore lattice, which hosts a pair of degenerate flat bands touching a dispersive band. We derive a three-orbital effective continuum model that captures the essential features near the band-touching point. Within this framework, we identify the point-like topological singularity on a planar manifold defined by the degenerate flat band eigenvectors. This singularity strongly influences the quantum geometry and results in a characteristic Landau level structure, where the levels spread over a finite energy range. We show that this structure reflects the underlying band reconstruction due to the orbital Zeeman effect, which lifts the flat band degeneracy and induces the Weyl-semimetal-like dispersion near the singularity. Our analysis reveals that the range of Landau level spreading is proportional to the quantum metric of each Zeeman-split band. We further demonstrate that adding a small dispersion via longer-range . Finally, we show that our approach extends naturally to systems with higher orbital angular momentum, indicating the robustness of these features in a broad class of three-dimensional flat band models. |
| title | Singular flat bands in three dimensions: Landau level spreading, quantum geometry, and Weyl reconstruction |
| topic | Mesoscale and Nanoscale Physics |
| url | https://arxiv.org/abs/2506.14154 |