The theory of topological-topological flat bands
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arXiv
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| Format: | Preprint |
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2026
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| _version_ | 1866912982727917568 |
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| author | Liu, Rui-Heng Hu, Jiangping Fang, Chen |
| author_facet | Liu, Rui-Heng Hu, Jiangping Fang, Chen |
| contents | Electronic flat bands have localized Wannier-like orbitals as zero modes. In the Lieb or the kagome models, the localized orbitals satisfy a topological condition that entails two non-contractible loop eigenstates along $x/y$-axis in real space, and one topological band touching point with other bands in momentum space. In these topological-flat bands, the Bloch state at the touching point is ill-defined, and so is any topological invariant for the entire band. We propose a new topological condition that the loop states in different directions be linearly dependent. Its satisfaction removes the singularity at the band touching point, and enforces nontrivial, well-defined topological invariants. Enforcing the new condition, we obtain topological-topological (top$^2$)-flat bands in 2D and 3D that have nontrivial invariants including the Chern numbers, the $\mathbb{Z}_2$ invariants, and the topological-crystalline invariants. Under small, generic interactions, top$^2$-flat bands flow to correlated topological insulators with a dynamically generated, symmetric mass term; and specially designed interacting models can have top$^2$-flat bands as exact zero modes. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2603_24672 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | The theory of topological-topological flat bands Liu, Rui-Heng Hu, Jiangping Fang, Chen Mesoscale and Nanoscale Physics Strongly Correlated Electrons Electronic flat bands have localized Wannier-like orbitals as zero modes. In the Lieb or the kagome models, the localized orbitals satisfy a topological condition that entails two non-contractible loop eigenstates along $x/y$-axis in real space, and one topological band touching point with other bands in momentum space. In these topological-flat bands, the Bloch state at the touching point is ill-defined, and so is any topological invariant for the entire band. We propose a new topological condition that the loop states in different directions be linearly dependent. Its satisfaction removes the singularity at the band touching point, and enforces nontrivial, well-defined topological invariants. Enforcing the new condition, we obtain topological-topological (top$^2$)-flat bands in 2D and 3D that have nontrivial invariants including the Chern numbers, the $\mathbb{Z}_2$ invariants, and the topological-crystalline invariants. Under small, generic interactions, top$^2$-flat bands flow to correlated topological insulators with a dynamically generated, symmetric mass term; and specially designed interacting models can have top$^2$-flat bands as exact zero modes. |
| title | The theory of topological-topological flat bands |
| topic | Mesoscale and Nanoscale Physics Strongly Correlated Electrons |
| url | https://arxiv.org/abs/2603.24672 |