Topological states in a non-Hermitian two-dimensional Su-Schrieffer-Heeger model

A non-Hermitian topological insulator with a real spectrum is interesting in the theory of non-Hermitian extension of topological systems. We find an experimentally realizable example of a two-dimensional non-Hermitian topological insulator with a real spectrum. We consider the two-dimensional Su-Schrieffer-Heeger (SSH) model with gain and loss. We introduce a non-Hermitian polarization vector to explore topological phase and show that topological edge states in the band gap exist in the system.