平帶系統作為實現新奇量子態的平臺，近年來受到了廣泛的關注。理論上，無限質量平帶的非色散特性將有望實現鐵磁性、高溫分數量子霍爾物理、拓撲/高溫超導、以及激子絕緣行為等電子關聯效應。近年來，二維摩爾異質結、體相量子材料、電路QED系統、光學晶格和光子晶體中平帶的實驗驗證使平帶物理領域得到了蓬勃發展。以kagome、Lieb、pyrochlore和dice晶格為代表的平帶模型早在30多年前就已被提出。

最近，理論研究已經將平帶模型擴展到diamond-octagon和Creutz等更加新奇的晶格，并引入了可以系統生成平帶晶格的通用模型。然而，這些晶體系統實驗上的實現還相對稀缺，且主要集中于kagome模型。因此，亟需對平帶研究進行擴展，識別具有其他晶格結構的候選材料。

來自麻省理工學院物理系的Joseph G. Checkelsky教授課題組，開發了一種高通量方法，通過對Materials Project數據庫中的候選材料建立簡單的（即只考慮最近鄰、單軌道、均勻躍遷）緊束縛模型來識別平帶系統。

Fig. 3 | Bandstructure and density of states for the most common lattices.

該方法能夠以較低的計算成本捕捉候選材料中平帶晶格結構的大部分基本特征，有助于識別材料系統并進行后續的詳細研究、以及模型系統的理論和超材料研究。他們將該算法應用于Materials Project數據庫中的139,367種材料，識別出其中有63,076種材料至少包含一個平帶元素子晶格。研究者進一步將這些候選系統分為至少31,635種獨特的平帶晶體網，并從晶格和能帶結構兩個角度識別出感興趣的候選材料。

作者的這項工作擴展了物理上可實現的晶體結構中已知的平帶晶格數量，并根據晶格結構對大部分系統進行了分類，為熟知的（如kagome、pyrochlore、Lieb和dice）和先前未知的晶格結構提供了額外的見解。該文近期發布于npj Computational Materials 10: 39 (2024).

Fig. 5 | Distorted lattices and higher symmetry flat band lattices.

Editorial Summary

Flat band systems have recently received significant attention as platforms to realize exotic quantum states. Theoretically, the non-dispersive nature of these infinitely massive flat bands may enable electronic correlation effects, including ferromagnetism, high-temperature fractional quantum Hall physics, topological and/or high-temperature superconductivity, and excitonic insulating behavior. The field of flat band physics has been recently invigorated by the experimental identification of flat electronic bands in 2D moiré heterostructures, bulk quantum materials, circuit QED systems, optical lattices, and photonic crystals. Flat band-hosting crystal lattices were proposed over 30 years ago, exemplified by models for the kagome, Lieb, pyrochlore, and dice lattices. More recent theoretical efforts have expanded flat band models to more exotic lattices such as the diamond-octagon and the Creutz, and introduced general models by which flat band lattices can be systematically generated. However, experimental realization in crystalline systems has been relatively scarce and has focused on the kagome prototype. There is therefore an opportunity to expand flat band studies with the identification of candidates for other lattice motifs.?

A?group led by Prof. Joseph G. Checkelsky from the Department of Physics, Massachusetts Institute of Technology, developed a high-throughput approach to identify flat band systems by building simple (i.e., nearest-neighbor, single orbital, uniform hopping) tight-binding models on candidates drawn from the Materials Project. This approach can capture many of the essential features relevant to identifying flat band lattice motifs in candidate materials in a computationally inexpensive manner, and is of use to identify systems for further detailed investigation as well as theoretical and metamaterials studies of model systems. They applied this algorithm to 139,367 materials in the Materials Project database and identified 63,076 materials that host at least one flat band elemental sublattice. They further categorized these candidate systems into at least 31,635 unique flat band crystal nets and identified candidates of interest from both lattice and band structure perspectives. This work expands the number of known flat band lattices that exist in physically realizable crystal structures and classifies the majority of these systems by the underlying lattice, providing additional insights for familiar (e.g., kagome, pyrochlore, Lieb, and dice) as well as previously unknown motifs. This article was recently published in npj Computational Materials 10: 39 (2024).

原文Abstract及其翻譯

Crystal net catalog of model flat band materials (模型平帶材料的晶體網目錄)

Paul M. Neves, Joshua P. Wakefield, Shiang Fang, Haimi Nguyen, Linda Ye & Joseph G. Checkelsky

Abstract Flat band systems are currently under intense investigation in quantum materials, optical lattices, and metamaterials. These efforts are motivated by potential realization of strongly correlated phenomena enabled by frustration-induced flat band dispersions; identification of candidate platforms plays an important role in these efforts. Here, we develop a high-throughput materials search for bulk crystalline flat bands by automated construction of uniform-hopping near-neighbor tight-binding models. We show that this approach captures many of the essential features relevant to identifying flat band lattice motifs in candidate materials in a computationally inexpensive manner, and is of use to identify systems for further detailed investigation as well as theoretical and metamaterials studies of model systems. We apply this algorithm to 139,367 materials in the Materials Project database and identify 63,076 materials that host at least one flat band elemental sublattice. We further categorize these candidate systems into at least 31,635 unique flat band crystal nets and identify candidates of interest from both lattice and band structure perspectives. This work expands the number of known flat band lattices that exist in physically realizable crystal structures and classifies the majority of these systems by the underlying lattice, providing additional insights for familiar (e.g., kagome, pyrochlore, Lieb, and dice) as well as previously unknown motifs.

摘要平帶系統目前在量子材料、光學晶格和超材料中得到了廣泛的研究，其動機在于阻挫誘導的平帶色散將有望實現強關聯現象。在這些研究中，候選材料的識別起著至關重要的作用。這里，我們開發了一種高通量材料搜索方法，通過自動構建均勻躍遷的近鄰緊束縛模型，搜索具有平帶結構的晶體材料。我們證明了該方法能夠以較低的計算成本捕捉到候選材料平帶結構中的大部分基本特征，并且可用于識別系統以開展進一步的詳細研究，以及模型系統的理論和超材料研究。我們將該算法應用于Materials Project數據庫中的139,367種材料，識別出其中有63,076種材料至少包含一個平帶元素子晶格。我們進一步將這些候選系統分為至少31,635種獨特的平帶晶體網，并從晶格和能帶結構兩個角度識別出感興趣的候選材料。這項工作擴展了物理上可實現的晶體結構中已知的平帶晶格數量，并根據晶格結構對大部分系統進行了分類，為熟知的（如kagome、pyrochlore、Lieb和dice）和先前未知的晶格結構提供了額外的見解。