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arXiv · 2305.19810

Hybrid higher-order skin-topological effect in hyperbolic lattices

Junsong Sun·Chang-An Li·Shiping Feng·Huaiming Guo
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Abstract

We investigate the non-Hermitian Haldane model on hyperbolic $\{8, 3\}$ and $\{12, 3\}$ lattices, and showcase its intriguing topological properties in the simultaneous presence of non-Hermitian effect and hyperbolic geometry. From bulk descriptions of the system, we calculate the real space non-Hermitian Chern numbers by generalizing the method from its Hermitian counterpart and present corresponding phase diagram of the model. For boundaries, we find that skin-topological modes appear in the range of the bulk energy gap under certain boundary conditions, which can be explained by an effective one-dimensional zigzag chain model mapped from hyperbolic lattice boundary. Remarkably, these skin-topological modes are localized at specific corners of the boundary, constituting a hybrid higher-order skin-topological effect on hyperbolic lattices.

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Junsong Sun, Chang-An Li, Shiping Feng, Huaiming Guo. 2023-05-31. Hybrid higher-order skin-topological effect in hyperbolic lattices. https://doi.org/10.1103/physrevb.108.075122

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