General construction and topological classification of crystalline flat bands
General construction and topological classification of crystalline flat bands
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DOI：
10.1038/s41567-021-01445-3
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发表时间：
2021-12-23
期刊：
影响因子：
19.6
通讯作者：
Bernevig, B. Andrei
中科院分区：
文献类型：
--
作者：
Calugaru, Dumitru;Chew, Aaron;Bernevig, B. Andrei
介绍了一种通用理论技术来识别具有平带的材料。应用拓扑量子化学为所有空间群中的这些平带提供了生成基础。物质的奇异相可以从强电子相互作用和非平凡拓扑之间的相互作用中出现。电子能带结构中具有非色散能带的材料（例如扭曲双层石墨烯）是强相互作用物理的主要候选材料。然而，用于在晶体中获得这些“平带”的现有理论模型对于实验实现来说往往限制太多。在这里，我们提出了一种从二分晶格构建完美平坦能带的通用理论技术。我们的规定封装并概括了文献中的各种平带模型，并且适用于具有任何轨道含量的系统，无论有或没有自旋轨道耦合。利用拓扑量子化学，我们根据所有有隙和平带的对称特征值建立了完整的拓扑分类。我们还推导了平坦能带和色散能带之间存在对称保护带接触点的标准，并将有间隙的平坦能带确定为脆弱拓扑相的主要候选者。最后，我们证明所有完全平坦能带的集合是有限生成的，并为所有 1,651 个 Shubnikov 空间群构造了相应的基。
A general theoretical technique is introduced to identify materials that host flat bands. Applying topological quantum chemistry provides the generating bases for these flat bands in all space groups.Exotic phases of matter can emerge from the interplay between strong electron interactions and non-trivial topology. Materials that have non-dispersing bands in their electronic band structure, such as twisted bilayer graphene, are prime candidates for strongly interacting physics. However, existing theoretical models for obtaining these 'flat bands' in crystals are often too restrictive for experimental realizations. Here we present a generic theoretical technique for constructing perfectly flat bands from bipartite crystalline lattices. Our prescription encapsulates and generalizes the various flat-band models in the literature and is applicable to systems with any orbital content, with or without spin-orbit coupling. Using topological quantum chemistry, we build a complete topological classification in terms of symmetry eigenvalues of all the gapped and gapless flat bands. We also derive criteria for the existence of symmetry-protected band touching points between the flat and dispersive bands, and identify the gapped flat bands as prime candidates for fragile topological phases. Finally, we show that the set of all perfectly flat bands is finitely generated and construct the corresponding bases for all 1,651 Shubnikov space groups.