双曲晶格中的拓扑平带
Topological flat bands in hyperbolic lattices
AI总结：
本工作研究了双曲kagome晶格中的拓扑平带，通过引入交错磁通和次近邻跃迁在多种晶格中实现了平带比超15的拓扑平带，并证实了硬核玻色子填充时存在ν=1/2的双曲分数量子霍尔绝缘体态。
摘要：
拓扑平带（TFBs）为研究诸如分数量子霍尔绝缘体（FCIs）等有趣的分数化现象提供了一个有前景的平台。大多数TFB模型都建立在曲率为零的二维欧几里得晶格中。在本工作中，我们系统地探讨了在一类具有恒定负曲率的二维非欧几里得晶格，即kagome晶格的双曲类似物中的TFBs。基于阿贝尔双曲能带理论，通过引入交错磁通和次近邻跃迁，分别在heptagon-kagome、octagon-kagome、nonagon-kagome和decagon-kagome晶格中发现了TFBs。所有双曲TFB模型的平带比均超过15，这表明在这些TFB模型中可以实现双曲FCIs。我们进一步证明了当硬核玻色子填充这些双曲TFB模型时，在开边界条件下存在ν=1/2的FCI态。
英文摘要：
Topological flat bands (TFBs) provide a promising platform to investigate intriguing fractionalization phenomena, such as the fractional Chern insulators (FCIs). Most of TFB models are established in two-dimensional Euclidean lattices with zero curvature. In this work, we systematically explore TFBs in a class of two-dimensional non-Euclidean lattices with constant negative curvature, {\emph i.e.,} the hyperbolic analogs of the kagome lattice. Based on the Abelian hyperbolic band theory, TFBs have been respectively found in the heptagon-kagome, the octagon-kagome, the nonagon-kagome and the decagon-kagome lattices by introducing staggered magnetic fluxes and the next nearest-neighbor hoppings. The flatness ratios of all hyperbolic TFB models are more than 15, which suggests that the hyperbolic FCIs can be realized in these TFB models. We further demonstrate the existence of a $ν=1/2$ FCI state with open boundary conditions when hard-core bosons fill into these hyperbolic TFB models.
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