Hybrid higher-order skin-topological effect in hyperbolic lattices

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.

arXiv comment10 pages, 10 figures

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• Hyperbolic Fractional Chern insulators
• Anderson transition and mobility edges on hyperbolic lattices with randomly connected boundaries
• Constraints of internal symmetry on the non-Hermitian skin effect and bidirectional skin effect under the action of the Hermitian conjugate of time-reversal symmetry
• Interaction-Induced Second-Order Skin Effect
• Hyperbolic Spin Liquids
• Non-Hermitian Skin Effect Along Hyperbolic Geodesics
• Non-Hermitian Quantum Fractals
• Inner non-Hermitian skin effect on Bethe lattice
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• Theory for the spectral splitting exponent of exceptional points
• Non-Hermitian higher-order topological insulators enabled by altermagnet engineering
• Hybrid Higher-Order Skin Topological Modes in the Two-Dimensional Su-Schrieffer-Heeger Model with Nonreciprocal Hoppings