title: Edge Modes, Degeneracies, and Topological Numbers in Non-Hermitian Systems.
abstract: 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.
authors.affiliation: Division of Physics and Applied Physics, School of Physical and Mathematical Sciences, Nanyang Technological University, Singapore 637371, Singapore.
authors.forename: Daniel
authors.initials: D
authors.lastname: Leykam
authors.affiliation: CEMS, RIKEN, Wako-shi, Saitama 351-0198, Japan.|Nonlinear Physics Centre, RSPE, The Australian National University, Canberra, Australian Capital Territory 0200, Australia.
authors.forename: Konstantin Y
authors.initials: KY
authors.lastname: Bliokh
authors.affiliation: Division of Physics and Applied Physics, School of Physical and Mathematical Sciences, Nanyang Technological University, Singapore 637371, Singapore.|Department of Physics, National Tsing Hua University, Hsinchu 30013, Taiwan.
authors.forename: Chunli
authors.initials: C
authors.lastname: Huang
authors.affiliation: Division of Physics and Applied Physics, School of Physical and Mathematical Sciences, Nanyang Technological University, Singapore 637371, Singapore.|Centre for Disruptive Photonic Technologies, Nanyang Technological University, Singapore 637371, Singapore.
authors.forename: Y D
authors.initials: YD
authors.lastname: Chong
authors.affiliation: CEMS, RIKEN, Wako-shi, Saitama 351-0198, Japan.|Physics Department, University of Michigan, Ann Arbor, Michigan 48109-1040, USA.
authors.forename: Franco
authors.initials: F
authors.lastname: Nori