Separable zero energy topological edge states and nonzero energy gap states in the nonreciprocal Su-Schrieffer-Heeger model

Complex energy eigenvalues and the non-Hermitian skin effect are two notable properties of non-Hermitian systems. These properties result in the localization of all eigenstates at the system boundaries, which can undermine the dynamic stability and experimental detection of topological edge states. In this paper, we investigate the one-dimensional non-Hermitian Su-Schrieffer-Heeger model with next-nearest-neighbor nonreciprocal hopping. By examining the energy spectrum and state distributions of the system, we demonstrate that the zero energy topological edge state and nonzero energy gap state can be distinguished from the non-Hermitian skin states. Additionally, we analyze the localization properties of these two states using the directional inverse participation ratio and investigate the non-Hermitian skin effect through the energy spectrum on the complex plane and the spectral winding number. Furthermore, we present phase diagrams of separation factor that illustrate the separation phenomenon between the edge or gap state and skin states. This work reveals the intriguing relationship between topological properties and non-Hermitian skin effects in one-dimensional nonreciprocal systems.