Work

Topological flat bands in hyperbolic lattices

Year: 2025

Type: article

Abstract: Topological flat bands (TFBs) provide a promising platform to investigate intriguing fractionalization phenomena, such as fractional Chern insulators (FCIs). Most TFB models are established in two-dimensional Euclidean lattices with zero curvature. In this paper, we systematically explore TFBs in a class of two-dimensional non-Euclidean lattices with constant negative curvature, i.e., the hyperbolic analogs of the kagome lattice. Based on 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 next-nearest-neighbor hoppings. The flatness ratios of all hyperbolic TFB models are more than 15, which suggests that hyperbolic FCIs can be realized in these TFB models. We further demonstrate the existence of a $\ensuremath{\nu}=1/2$ FCI state with open boundary conditions when hard-core bosons fill into these hyperbolic TFB models.

Source: Physical review. B./Physical review. B

DOI: 10.1103/physrevb.111.165144

Authors: Dong-Hao Guan, Lu Qi, Yuan Zhou, Ai-Lei He, Yi-Fei Wang

Institutions: National Laboratory of Solid State Microstructures, Yangzhou University, Nanjing University, Zhejiang Normal University

Language: English

Topic: Topological Materials and Phenomena

Subfield: Atomic and Molecular Physics, and Optics

Field: Physics and Astronomy

Domain: Physical Sciences

Open Access status: green

Funders: National Natural Science Foundation of China, Government of Jiangsu Province, Natural Science Foundation of Jiangsu Province

Awards: G5137242825, G551224978, G8413604445, G97137270