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

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

Research output: Contribution to journalArticlepeer-review

496 Scopus citations


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 existence of these edge modes is intimately related to exceptional points of the bulk Hamiltonians, i.e., degeneracies in the bulk spectra of the media. We find that the topological edge modes can be divided into three families ("Hermitian-like," "non-Hermitian," and "mixed"); these are characterized by two winding numbers, describing two distinct kinds of half-integer charges carried by the exceptional points. We show that all the above types of topological edge modes can be realized in honeycomb lattices of ring resonators with asymmetric or gain-loss couplings.

Original languageEnglish
Article number040401
JournalPhysical Review Letters
Issue number4
StatePublished - Jan 23 2017

Bibliographical note

Funding Information:
This research was supported by the Singapore National Research Foundation (Grant No. NRFF2012-02), the Singapore Ministry of Education (MOE) Academic Research Fund Tier 2 (Grant No. MOE2015-T2-2-008), the RIKEN Interdisciplinary Theoretical Science Research Group (iTHES) Project, the Multi-University Research Initiative (MURI) Center for Dynamic Magneto-Optics via the Air Force Office of Scientific Research (AFOSR) (Grant No. FA9550-14-1-0040), Grant-in-Aid for Scientific Research (A), Core Research for Evolutionary Science and Technology (CREST), the John Templeton Foundation, and the Australian Research Council.

Publisher Copyright:
© 2017 American Physical Society.

ASJC Scopus subject areas

  • Physics and Astronomy (all)


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