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

TL;DR

This paper classifies and interprets two-dimensional non-Hermitian topological phases, revealing novel edge phenomena such as infernal points and exceptional point dispersions that extend understanding beyond the skin effect.

Contribution

It derives physical bulk-boundary correspondence for all 2D non-Hermitian point gap phases, identifying new edge states and spectral flow phenomena.

Findings

Discovery of infernal points with localized skin effect

Identification of non-Hermitian exceptional point dispersions

Edge states with well-defined dispersion along all boundary terminations

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.