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We analyze chiral topological edge modes in a non-Hermitian variant of the 2DDirac equation. Such modes appear at interfaces between media with different"masses" and/or signs of the "non-Hermitian charge". The existence of theseedge modes is intimately related to exceptional points of the bulkHamiltonians, i.e., degeneracies in the bulk spectra of the media. We find thatthe topological edge modes can be divided into three families("Hermitian-like", "non-Hermitian", and "mixed"), these are characterized bytwo winding numbers, describing two distinct kinds of half-integer chargescarried by the exceptional points. We show that all the above types oftopological edge modes can be realized in honeycomb lattices of ring resonatorswith asymmetric or gain/loss couplings.

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