Topological edge states in Su-Schrieffer-Heeger chain via non-Hermitian coupling

Abstract

We study the effect of non-Hermition coupling on topological and Hermitian characteristics in a non-Hermitian Su-Schrieffer-Heeger (SSH) chain. Different effects on the properties of the eigenvalues spectrum in topologically trivial and nontrivial phases are presented. The odevity of the number of lattices is also considered. We find that in the even number lattices case the system undergoes an abrupt transition from the Hermitian states to non-Hermitian states at a certain critical point when increasing the strength of the imaginary potential in non-Hermitian coupling. But in the odd number lattices case the “critical points” are actually pseudo critical points, which is proved by the amplitudes distributions calculated by coupled mode theory (CMT).