Ideal topological flat bands in chiral symmetric moiré systems from non-holomorphic functions

Siddhartha Sarkar, Xiaohan Wan, Yitong Zhang and Kai Sun ()
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Siddhartha Sarkar: University of Michigan
Xiaohan Wan: University of Michigan
Yitong Zhang: University of Michigan
Kai Sun: University of Michigan

Nature Communications, 2025, vol. 16, issue 1, 1-7

Abstract: 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 fk(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.

Date: 2025
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DOI: 10.1038/s41467-025-62222-x

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