非阿贝尔线图：一种实现平坦带的通用方法
Non-Abelian line graph: A generalized approach to flat bands
AI总结：
本文提出非阿贝尔线图理论，通过引入多重线图结构，实现包含更高角动量轨道和自旋轨道耦合的平坦带，拓展了传统s轨道模型的应用范围。
摘要：
材料中的平坦带（FBs）可以增强相关效应，产生奇特现象。线图（LG）晶格以其在s轨道模型中宿主平坦带而闻名。尽管在Kagome金属中广泛应用，但将更高角动量轨道与自旋轨道耦合（SOCs）纳入LG以实现FBs的通用方法仍缺乏。本文引入非阿贝尔LG理论，构造现实系统中的FBs，结合内部自由度，超越s轨道模型。通过修改LG的晶格边和站点为任意Hermitian矩阵，称为多重LG。关键方面是将多重LG哈密顿量映射到尊重晶格对称性的紧束缚（TB）模型中，通过适当局部非阿贝尔变换。我们建立了确定局部变换的一般条件。基于此机制，我们在Kagome晶格中演示了d轨道FB的实现，可能作为理解过渡金属Kagome材料中FB的最小模型。我们的方法弥合了纯晶格模型中已知FB与多轨道系统中实现FB之间的差距。
英文摘要：
Flat bands (FBs) in materials can enhance the correlation effects, resulting in exotic phenomena. Line graph (LG) lattices are well known for hosting FBs with isotropic hoppings in $s$-orbital models. Despite their prevalent application in the Kagome metals, there has been a lack of a general approach for incorporating higher-angular-momentum orbitals with spin-orbit couplings (SOCs) into LGs to achieve FBs. Here, we introduce a non-Abelian LG theory to construct FBs in realistic systems, which incorporates internal degrees of freedom and goes beyond $s$-orbital models. We modify the lattice edges and sites in the LG to be associated with arbitrary Hermitian matrices, referred to as the multiple LG. A fundamental aspect involves mapping the multiple LG Hamiltonian to a tight-binding (TB) model that respects the lattice symmetry through appropriate local non-Abelian transformations. We establish the general conditions to determine the local transformations. Based on this mechanism, we demonstrate the realization of $d$-orbital FBs in the Kagome lattice, which could serve as a minimal model for understanding the FBs in transition metal Kagome materials. Our approach bridges the gap between the known FBs in pure lattice models and their realization in multi-orbital systems.
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