Lee, Tony E.2016-11-152016-11-152016-04Lee, T. E. (2016). Anomalous Edge State in a Non-Hermitian Lattice. Physical Review Letters, 116(13), 133903. https://doi.org/10.1103/PhysRevLett.116.133903https://hdl.handle.net/1805/11457We show that the bulk-boundary correspondence for topological insulators can be modified in the presence of non-Hermiticity. We consider a one-dimensional tight-binding model with gain and loss as well as long-range hopping. The system is described by a non-Hermitian Hamiltonian that encircles an exceptional point in momentum space. The winding number has a fractional value of 1/2. There is only one dynamically stable zero-energy edge state due to the defectiveness of the Hamiltonian. This edge state is robust to disorder due to protection by a chiral symmetry. We also discuss experimental realization with arrays of coupled resonator optical waveguides.enPublisher Policytopological insulatorsnon-HermiticityArticle