Truncation-dependent PT phase transition for the edge states of a two-dimensional non-Hermitian system

Abstract

We consider a bulk system supporting parity and time reversal ($PT$) symmetry, and investigate how the $PT$ phase transition of edge states is influenced by different truncations of the system. As an example, we study a two-dimensional $PT$-symmetric Su--Schrieffer--Heeger lattice with non-Hermitian onsite potentials. We find that when the truncation preserves certain symmetries of the bulk lattice, the edge states can remain in the $PT$-unbroken phase when the non-Hermitian onsite potentials are less than a nonzero critical value. On the other hand, when the truncation removes such symmetries, edge states with complex eigen-energies are observed for infinitesimal non-Hermitian onsite potentials. We develop an analytic theory to account for such behaviors. Our results are important in the manipulation of the gain and loss behaviors of edge states in non-Hermitian systems, with potential applications in the study of topological lasers, quantum sensors, and unidirectional invisibility.