Hybrid higher-order skin-topological effect in hyperbolic lattices

TL;DR

This paper explores the interplay of non-Hermitian effects and hyperbolic geometry in topological lattices, revealing unique skin-topological modes localized at corners, which extend the understanding of higher-order topological phenomena.

Contribution

It introduces a generalized method for calculating non-Hermitian Chern numbers on hyperbolic lattices and uncovers hybrid higher-order skin-topological modes.

Findings

Skin-topological modes appear in the bulk energy gap.

Modes are localized at specific corners of the boundary.

The study extends topological concepts to hyperbolic geometries.

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.