Topological flat bands in hyperbolic Haldane models

Topological flat bands (TFBs) play a crucial role in the realization of fractional Chern insulators (FCIs) and various TFB models have been constructed in two-dimensional Euclidean lattice models. Recently, the notion of TFBs has been extended to the hyperbolic analogs of kagome lattices, which provide a promising platform to investigate the interplay of the non-Euclidean geometry and FCIs. In this work, we demonstrate the existence of TFBs in hyperbolic Haldane models, the generalizations of the Haldane model proposed in the Euclidean honeycomb lattice. Based on the Abelian hyperbolic band theory, TFBs with large flatness ratios are found by tuning hopping parameters up to the third nearest neighbors. These TFBs still exist in more than ${10}^{8}\text{\ensuremath{-}}\mathrm{site}$ systems with open boundary conditions, which reveals the robustness of TFBs in hyperbolic Haldane models. We further investigate the $\ensuremath{\nu}=1/2$ FCI when considering hard-core bosons loaded into these hyperbolic TFBs. Our studies provide an alternative platform to realize TFBs and subsequent FCIs beyond the Euclidean lattices.