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

Kazuki Sone,Yuto Ashida,Takahiro Sagawa

doi:10.1038/s41467-020-19488-0

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 lattice 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.

Highlights

Topological materials exhibit edge-localized scattering-free modes protected by their nontrivial bulk topology through the bulk-edge correspondence in Hermitian systems
We reveal a ubiquitous mechanism for realizing robust gapless edge modes, which emerge independently of the bulk topology and instead are protected in an unconventional manner unique to non-Hermitian systems
We explicitly show the existence of exceptional edge modes in a more realistic system based on active matter[46], which is a collection of self-propelled particles and has recently attracted much interest as a useful platform to study biological and out-of-equilibrium physics

Summary

Introduction

Topological materials exhibit edge-localized scattering-free modes protected by their nontrivial bulk topology through the bulk-edge correspondence in Hermitian systems. We reveal that, in non-Hermitian systems, robust gapless edge modes can ubiquitously appear owing to a mechanism that is distinct from bulk topology, 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. We reveal a ubiquitous mechanism for realizing robust gapless edge modes, which emerge independently of the bulk topology and instead are protected in an unconventional manner unique to non-Hermitian systems This indicates that the bulk-based classification cannot conclusively predict the existence or absence of edge modes in the non-Hermitian case, implying the breakdown of the bulk-edge correspondence. We demonstrate that this type of non-Hermitian chiral active matter provides an ideal platform to experimentally realize the proposed exceptional edge modes

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Results

Conclusion