Edge Modes, Degeneracies, and Topological Numbers in Non-Hermitian Systems

Daniel Leykam, Konstantin Y. Bliokh, Chunli Huang, Y. D. Chong, Franco Nori

Published 2016-10-13Version 1

We analyze chiral topological edge modes in a non-Hermitian variant of the 2D Dirac equation. Such modes appear at interfaces between media with different "masses" and/or signs of the "non-Hermitian charge". The appearance and regions of existence of the edge modes are intimately related to exceptional points, i.e., degeneracies in the bulk spectra of the media. We find that the topological edge modes can be divided into three classes ("Hermitian-like", "non-Hermitian", and "mixed"), and these are described by two winding numbers corresponding to a pair of half-integer charges carried by exceptional points of the bulk Hamiltonian. We also show that the non-Hermitian topological edge modes can be realized in a honeycomb-like lattice of ring resonators with non-Hermitian couplings.