Exceptional non-Hermitian topological edge mode and its application to active matter

TL;DR

This paper uncovers a new type of robust, gapless edge mode in non-Hermitian systems, driven by branchpoint singularities near exceptional points, with applications in active matter and non-Hermitian device design.

Contribution

It introduces a novel topological mechanism for edge modes in non-Hermitian systems, independent of bulk topology, based on branchpoint singularities at exceptional points.

Findings

Edge modes arise from branchpoint singularities, not bulk topology.

These modes are robust and can be used for lasing wave packets.

Active matter models exhibit these non-Hermitian topological features.

Abstract

Topological materials exhibit edge-localized scattering-free modes protected by their nontrivial bulk topology through the bulk-edge correspondence in Hermitian systems. While topological phenomena have recently been much investigated in non-Hermitian systems with dissipations and injections, the fundamental principle of their edge modes has not fully been established. Here, we reveal that in non-Hermitian systems robust gapless edge modes can ubiquitously appear owing to a mechanism that is distinct from bulk topology, thus indicating the breakdown of the bulk-edge correspondence. The robustness of these edge modes originates from yet another topological structure accompanying the branchpoint singularity around an exceptional point, at which eigenvectors coalesce and the Hamiltonian becomes nondiagonalizable. Their characteristic complex eigenenergy spectra are applicable to realize lasing wave packets that propagate along the edge of the sample. We numerically confirm the emergence and the robustness of the proposed edge modes in the prototypical models. Furthermore, we show that these edge modes appear in a model of chiral active matter based on the hydrodynamic description, demonstrating that active matter can exhibit an inherently non-Hermitian topological feature. The proposed general mechanism would serve as an alternative designing principle to realize scattering-free edge current in non-Hermitian devices, going beyond the existing frameworks of non-Hermitian topological phases.