Ideal topological flat bands in chiral symmetric moir\'e systems from non-holomorphic functions

TL;DR

This paper introduces a new family of ideal topological flat bands in chiral symmetric moiré systems, where the wavefunctions are constructed from non-holomorphic functions, expanding the understanding beyond traditional holomorphic structures.

Contribution

It presents a novel class of topological flat bands using non-holomorphic functions, along with models, principles, and an analytic method for wavefunction construction.

Findings

Wavefunctions with non-holomorphic functions exhibit ideal quantum geometry.

Constructed flat bands have Chern numbers of ±2 or higher.

Universal principles and methods for designing these bands are provided.

Abstract

Recent studies on topological flat bands and their fractional states have revealed increasing similarities between moir\'e 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, $\psi_{\mathbf{k}} = f_{\mathbf{k}-\mathbf{k}_0}(z) \psi_{\mathbf{k}_0}$, where $f_{\mathbf{k}}(z)$ is a holomorphic function. This holomorphic structure has been the foundation of existing knowledge on constructing ideal topological flat bands. In this Letter, 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 $C = \pm 2$ or higher.