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

Bulk band topology is recently much studied in non-Hermitian physics, while its correspondence to the existence of edge modes is more subtle than the Hermitian case. Here, we reveal that gapless edge modes can be protected by topology and symmetry of the band structure of edge modes themselves around the branchpoint singularity of exceptional points [1]. Such gapless edge modes, which we termed as exceptional edge modes, are robust independently of the bulk topology, thus implying the breakdown of the bulk-edge correspondence in non-Hermitian systems. We numerically confirm the emergence and robustness of exceptional edge modes in a simple model with topologically trivial bulk. We also propose the applications of exceptional edge modes to a topological insulator laser and chiral active matter.
[1] K. Sone, Y. Ashida, and T. Sagawa, arXiv:1912.09055 (to appear in Nature Communications).