Infernal and Exceptional Edge Modes: Non-Hermitian Topology Beyond the Skin Effect

• URL: http://arxiv.org/abs/2304.13743v2
• Date: Fri, 1 Sep 2023 15:30:33 GMT
• Title: Infernal and Exceptional Edge Modes: Non-Hermitian Topology Beyond the Skin Effect
• Authors: M. Michael Denner, Titus Neupert, Frank Schindler
• Abstract summary: We derive the edge signatures of all two-dimensional phases with intrinsic point gap topology. We find two broad classes of non-Hermitian edge states: (1) Infernal points, where a skin effect occurs only at a single edge momentum, while all other edge momenta are devoid of edge states. Surprisingly, the latter class of systems allows for a finite, non-extensive number of edge states with a well defined dispersion along all generic edge terminations.
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• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: The classification of point gap topology in all local non-Hermitian symmetry classes has been recently established. However, many entries in the resulting periodic table have only been discussed in a formal setting and still lack a physical interpretation in terms of their bulk-boundary correspondence. Here, we derive the edge signatures of all two-dimensional phases with intrinsic point gap topology. While in one dimension point gap topology invariably leads to the non-Hermitian skin effect, non-Hermitian boundary physics is significantly richer in two dimensions. We find two broad classes of non-Hermitian edge states: (1) Infernal points, where a skin effect occurs only at a single edge momentum, while all other edge momenta are devoid of edge states. Under semi-infinite boundary conditions, the point gap thereby closes completely, but only at a single edge momentum. (2) Non-Hermitian exceptional point dispersions, where edge states persist at all edge momenta and furnish an anomalous number of symmetry-protected exceptional points. Surprisingly, the latter class of systems allows for a finite, non-extensive number of edge states with a well defined dispersion along all generic edge terminations. Instead, the point gap only closes along the real and imaginary eigenvalue axes, realizing a novel form of non-Hermitian spectral flow.

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