Ideal topological flat bands in chiral symmetric moiré systems from non-holomorphic functions.
basic_science · Level V
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- Record sourced from PubMed, PMID 40750793.
- Also identified by DOI 10.1038/s41467-025-62222-x and PMC identifier 12317057.
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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, <math xmlns="http://www.w3.org/1998/Math/MathML"> <msub><mrow><mi>ψ</mi></mrow> <mrow><mi>k</mi></mrow> </msub> <mo>=</mo> <msub><mrow><mi>f</mi></mrow> <mrow><mi>k</mi> <mo>-</mo> <msub><mrow><mi>k</mi></mrow> <mrow><mn>0</mn></mrow> </msub> </mrow> </msub> <mrow><mo>(</mo> <mrow><mi>z</mi></mrow> <mo>)</mo></mrow> <msub><mrow><mi>ψ</mi></mrow> <mrow> <msub><mrow><mi>k</mi></mrow> <mrow><mn>0</mn></mrow> </msub> </mrow> </msub> </math> , where f<sub>k</sub>(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.