The flattening of single-particle band structures plays an important role in the quest for novel quantum states of matter owing to the crucial role of interactions. Recent advances in theory and experiment made it possible to construct and tune systems with nearly flat bands, ranging from graphene multilayers and moiré materials to kagome metals and ruthenates. Although theoretical models predict exactly flat bands under certain ideal conditions, evidence was provided that these systems host high-order Van Hove points, i.e., points of high local band flatness and power-law divergence in energy of the density of states. In this review, we examine recent developments in engineering and realizing such weakly dispersive bands. We focus on high-order Van Hove singularities and explore their connection to exactly flat bands. We provide classification schemes and discuss interaction effects. We also review experimental evidence for high-order Van Hove singularities and point out future research directions.

中文翻译：

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高阶 Van Hove 奇点及其与平坦带的联系


由于相互作用的关键作用，单粒子能带结构的扁平化在寻求物质的新量子态中起着重要作用。理论和实验的最新进展使得构建和调整具有近乎平坦带的系统成为可能，范围从石墨烯多层和莫尔材料到笼目金属和钌酸盐。尽管理论模型在某些理想条件下精确地预测了平坦带，但提供了证据表明这些系统承载高阶范霍夫点，即具有高局部频带平坦度和状态密度能量幂律发散的点。在这篇综述中，我们研究了工程学的最新发展并实现了这种弱色散带。我们专注于高阶范霍夫奇点，并探索它们与完全平坦带的联系。我们提供分类方案并讨论交互作用。我们还回顾了高阶 Van Hove 奇点的实验证据，并指出了未来的研究方向。