平帶系統(tǒng)作為實(shí)現(xiàn)新奇量子態(tài)的平臺(tái)，近年來(lái)受到了廣泛的關(guān)注。理論上，無(wú)限質(zhì)量平帶的非色散特性將有望實(shí)現(xiàn)鐵磁性、高溫分?jǐn)?shù)量子霍爾物理、拓?fù)?/span>/高溫超導(dǎo)、以及激子絕緣行為等電子關(guān)聯(lián)效應(yīng)。近年來(lái)，二維摩爾異質(zhì)結(jié)、體相量子材料、電路QED系統(tǒng)、光學(xué)晶格和光子晶體中平帶的實(shí)驗(yàn)驗(yàn)證使平帶物理領(lǐng)域得到了蓬勃發(fā)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(jīng)將平帶模型擴(kuò)展到diamond-octagon和Creutz等更加新奇的晶格，并引入了可以系統(tǒng)生成平帶晶格的通用模型。然而，這些晶體系統(tǒng)實(shí)驗(yàn)上的實(shí)現(xiàn)還相對(duì)稀缺，且主要集中于kagome模型。因此，亟需對(duì)平帶研究進(jìn)行擴(kuò)展，識(shí)別具有其他晶格結(jié)構(gòu)的候選材料。

來(lái)自麻省理工學(xué)院物理系的Joseph G. Checkelsky教授課題組，開(kāi)發(fā)了一種高通量方法，通過(guò)對(duì)Materials Project數(shù)據(jù)庫(kù)中的候選材料建立簡(jiǎn)單的（即只考慮最近鄰、單軌道、均勻躍遷）緊束縛模型來(lái)識(shí)別平帶系統(tǒng)。

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

該方法能夠以較低的計(jì)算成本捕捉候選材料中平帶晶格結(jié)構(gòu)的大部分基本特征，有助于識(shí)別材料系統(tǒng)并進(jìn)行后續(xù)的詳細(xì)研究、以及模型系統(tǒng)的理論和超材料研究。他們將該算法應(yīng)用于Materials Project數(shù)據(jù)庫(kù)中的139,367種材料，識(shí)別出其中有63,076種材料至少包含一個(gè)平帶元素子晶格。研究者進(jìn)一步將這些候選系統(tǒng)分為至少31,635種獨(dú)特的平帶晶體網(wǎng)，并從晶格和能帶結(jié)構(gòu)兩個(gè)角度識(shí)別出感興趣的候選材料。

作者的這項(xiàng)工作擴(kuò)展了物理上可實(shí)現(xiàn)的晶體結(jié)構(gòu)中已知的平帶晶格數(shù)量，并根據(jù)晶格結(jié)構(gòu)對(duì)大部分系統(tǒng)進(jìn)行了分類(lèi)，為熟知的（如kagome、pyrochlore、Lieb和dice）和先前未知的晶格結(jié)構(gòu)提供了額外的見(jiàn)解。該文近期發(fā)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(wǎng)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(tǒng)目前在量子材料、光學(xué)晶格和超材料中得到了廣泛的研究，其動(dòng)機(jī)在于阻挫誘導(dǎo)的平帶色散將有望實(shí)現(xiàn)強(qiáng)關(guān)聯(lián)現(xiàn)象。在這些研究中，候選材料的識(shí)別起著至關(guān)重要的作用。這里，我們開(kāi)發(fā)了一種高通量材料搜索方法，通過(guò)自動(dòng)構(gòu)建均勻躍遷的近鄰緊束縛模型，搜索具有平帶結(jié)構(gòu)的晶體材料。我們證明了該方法能夠以較低的計(jì)算成本捕捉到候選材料平帶結(jié)構(gòu)中的大部分基本特征，并且可用于識(shí)別系統(tǒng)以開(kāi)展進(jìn)一步的詳細(xì)研究，以及模型系統(tǒng)的理論和超材料研究。我們將該算法應(yīng)用于Materials Project數(shù)據(jù)庫(kù)中的139,367種材料，識(shí)別出其中有63,076種材料至少包含一個(gè)平帶元素子晶格。我們進(jìn)一步將這些候選系統(tǒng)分為至少31,635種獨(dú)特的平帶晶體網(wǎng)，并從晶格和能帶結(jié)構(gòu)兩個(gè)角度識(shí)別出感興趣的候選材料。這項(xiàng)工作擴(kuò)展了物理上可實(shí)現(xiàn)的晶體結(jié)構(gòu)中已知的平帶晶格數(shù)量，并根據(jù)晶格結(jié)構(gòu)對(duì)大部分系統(tǒng)進(jìn)行了分類(lèi)，為熟知的（如kagome、pyrochlore、Lieb和dice）和先前未知的晶格結(jié)構(gòu)提供了額外的見(jiàn)解。