平带系统作为实现新奇量子态的平台，近年来受到了广泛的关注。理论上，无限质量平带的非色散特性将有望实现铁磁性、高温分数量子霍尔物理、拓扑/高温超导、以及激子绝缘行为等电子关联效应。近年来，二维摩尔异质结、体相量子材料、电路QED系统、光学晶格和光子晶体中平带的实验验证使平带物理领域得到了蓬勃发展。以kagome、Lieb、pyrochlore和dice晶格为代表的平带模型早在30多年前就已被提出。
Fig. 1 | Flowchart of the tight-binding flat band search algorithm.
最近，理论研究已经将平带模型扩展到diamond-octagon和Creutz等更加新奇的晶格，并引入了可以系统生成平带晶格的通用模型。然而，这些晶体系统实验上的实现还相对稀缺，且主要集中于kagome模型。因此，亟需对平带研究进行扩展，识别具有其他晶格结构的候选材料。
Fig. 2 | The twenty-one most common non-trivial flat band lattices.
来自麻省理工学院物理系的Joseph G. Checkelsky教授课题组，开发了一种高通量方法，通过对Materials Project数据库中的候选材料建立简单的（即只考虑最近邻、单轨道、均匀跃迁）紧束缚模型来识别平带系统。
Fig. 3 | Bandstructure and density of states for the most common lattices.
该方法能够以较低的计算成本捕捉候选材料中平带晶格结构的大部分基本特征，有助于识别材料系统并进行后续的详细研究、以及模型系统的理论和超材料研究。他们将该算法应用于Materials Project数据库中的139,367种材料，识别出其中有63,076种材料至少包含一个平带元素子晶格。研究者进一步将这些候选系统分为至少31,635种独特的平带晶体网，并从晶格和能带结构两个角度识别出感兴趣的候选材料。
Fig. 4 | Relations between flat band lattices in the kagome families.
作者的这项工作扩展了物理上可实现的晶体结构中已知的平带晶格数量，并根据晶格结构对大部分系统进行了分类，为熟知的（如kagome、pyrochlore、Lieb和dice）和先前未知的晶格结构提供了额外的见解。该文近期发布于npj Computational Materials 10: 39 (2024).
Fig. 5 | Distorted lattices and higher symmetry flat band lattices.
Editorial Summary
High-throughput discovering flat-band systems: Crystal net catalog
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及其翻译
Crystal net catalog of model flat band materials (模型平带材料的晶体网目录)
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 平带系统目前在量子材料、光学晶格和超材料中得到了广泛的研究，其动机在于阻挫诱导的平带色散将有望实现强关联现象。在这些研究中，候选材料的识别起着至关重要的作用。这里，我们开发了一种高通量材料搜索方法，通过自动构建均匀跃迁的近邻紧束缚模型，搜索具有平带结构的晶体材料。我们证明了该方法能够以较低的计算成本捕捉到候选材料平带结构中的大部分基本特征，并且可用于识别系统以开展进一步的详细研究，以及模型系统的理论和超材料研究。我们将该算法应用于Materials Project数据库中的139,367种材料，识别出其中有63,076种材料至少包含一个平带元素子晶格。我们进一步将这些候选系统分为至少31,635种独特的平带晶体网，并从晶格和能带结构两个角度识别出感兴趣的候选材料。这项工作扩展了物理上可实现的晶体结构中已知的平带晶格数量，并根据晶格结构对大部分系统进行了分类，为熟知的（如kagome、pyrochlore、Lieb和dice）和先前未知的晶格结构提供了额外的见解。