Ideal topological flat bands in chiral symmetric moiré systems from non-holomorphic functions
Abstract Recent studies on topological flat bands and their fractional states have revealed increasing similarities between moiré flat bands and Landau levels (LLs). For instance, like the lowest LL, topological exact flat bands with ideal quantum geometry can be constructed using the same holomorph...
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| Format: | Article |
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Nature Portfolio
2025-08-01
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| Series: | Nature Communications |
| Online Access: | https://doi.org/10.1038/s41467-025-62222-x |
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| author | Siddhartha Sarkar Xiaohan Wan Yitong Zhang Kai Sun |
| author_facet | Siddhartha Sarkar Xiaohan Wan Yitong Zhang Kai Sun |
| author_sort | Siddhartha Sarkar |
| collection | DOAJ |
| description | Abstract Recent studies on topological flat bands and their fractional states have revealed increasing similarities between moiré flat bands and Landau levels (LLs). For instance, like the lowest LL, topological exact flat bands with ideal quantum geometry can be constructed using the same holomorphic function structure, $${\psi }_{{{\bf{k}}}}={f}_{{{\bf{k}}}-{{{\bf{k}}}}_{0}}(z){\psi }_{{{{\bf{k}}}}_{0}}$$ ψ k = f k − k 0 ( z ) ψ k 0 , where f k (z) is a holomorphic function. This holomorphic structure has been the foundation of existing knowledge on constructing ideal topological flat bands. In this article, we report a new family of ideal topological flat bands where the f function does not need to be holomorphic. We provide both model examples and universal principles, as well as an analytic method to construct the wavefunctions of these flat bands, revealing their universal properties, including ideal quantum geometry and a Chern number of C = ±2 or higher. |
| format | Article |
| id | doaj-art-2e64a72d64e0415dbfeacf749ed7aff3 |
| institution | DOAJ |
| issn | 2041-1723 |
| language | English |
| publishDate | 2025-08-01 |
| publisher | Nature Portfolio |
| record_format | Article |
| series | Nature Communications |
| spelling | doaj-art-2e64a72d64e0415dbfeacf749ed7aff32025-08-20T03:05:06ZengNature PortfolioNature Communications2041-17232025-08-011611710.1038/s41467-025-62222-xIdeal topological flat bands in chiral symmetric moiré systems from non-holomorphic functionsSiddhartha Sarkar0Xiaohan Wan1Yitong Zhang2Kai Sun3Department of Physics, University of MichiganDepartment of Physics, University of MichiganDepartment of Physics, University of MichiganDepartment of Physics, University of MichiganAbstract Recent studies on topological flat bands and their fractional states have revealed increasing similarities between moiré flat bands and Landau levels (LLs). For instance, like the lowest LL, topological exact flat bands with ideal quantum geometry can be constructed using the same holomorphic function structure, $${\psi }_{{{\bf{k}}}}={f}_{{{\bf{k}}}-{{{\bf{k}}}}_{0}}(z){\psi }_{{{{\bf{k}}}}_{0}}$$ ψ k = f k − k 0 ( z ) ψ k 0 , where f k (z) is a holomorphic function. This holomorphic structure has been the foundation of existing knowledge on constructing ideal topological flat bands. In this article, we report a new family of ideal topological flat bands where the f function does not need to be holomorphic. We provide both model examples and universal principles, as well as an analytic method to construct the wavefunctions of these flat bands, revealing their universal properties, including ideal quantum geometry and a Chern number of C = ±2 or higher.https://doi.org/10.1038/s41467-025-62222-x |
| spellingShingle | Siddhartha Sarkar Xiaohan Wan Yitong Zhang Kai Sun Ideal topological flat bands in chiral symmetric moiré systems from non-holomorphic functions Nature Communications |
| title | Ideal topological flat bands in chiral symmetric moiré systems from non-holomorphic functions |
| title_full | Ideal topological flat bands in chiral symmetric moiré systems from non-holomorphic functions |
| title_fullStr | Ideal topological flat bands in chiral symmetric moiré systems from non-holomorphic functions |
| title_full_unstemmed | Ideal topological flat bands in chiral symmetric moiré systems from non-holomorphic functions |
| title_short | Ideal topological flat bands in chiral symmetric moiré systems from non-holomorphic functions |
| title_sort | ideal topological flat bands in chiral symmetric moire systems from non holomorphic functions |
| url | https://doi.org/10.1038/s41467-025-62222-x |
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