An unusual phase transition in a non-Hermitian Su-Schrieffer-Heeger model

TL;DR

This paper investigates a non-Hermitian SSH model with staggered Hermitian and non-Hermitian dimers, revealing unusual phase transitions and topological properties influenced by non-Hermiticity, including the stabilization of non-trivial phases and the behavior of edge states.

Contribution

It uncovers a novel phase transition mechanism in a non-Hermitian SSH model, showing how non-Hermiticity induces transitions between non-trivial insulating phases via semi-metallic states.

Findings

Complex eigenspectra for all non-zero non-Hermiticity

Stabilization of non-trivial insulating phase at high loss-gain

Unusual transition between non-trivial phases through semi-metallic phase

Abstract

This article studies a non-Hermitian Su-Schrieffer-Heeger (SSH) model which has periodically staggered Hermitian and non-Hermitian dimers. The changes in topological phases of the considered chiral symmetric model with respect to the introduced non-Hermiticity are studied where we find that the system supports only complex eigenspectra for all values of $u \neq 0$ and it stabilizes only non-trivial insulating phase for higher loss-gain strength. Even if the system acts as a trivial insulator in the Hermitian limit, the increase in loss-gain strength induces phase transition to non-trivial insulating phase through a (gapless) semi-metallic phase. Interesting phenomenon is observed in the case where Hermitian system acts as a non-trivial insulator. In such a situation, the introduced non-Hermiticity neither leaves the non-trivial phase undisturbed nor induces switching to trivial phase. Rather, it shows transition from non-trivial insulating phase to the same where it is mediated by the stabilization of (non-trivial) semi-metallic phase. This unusual transition between the non-trivial insulating phases through non-trivial semi-metallic phase gives rise to a question regarding the topological states of the system under open boundary conditions. So, we analyze the possibility of stable edge states in these two non-trivial insulating phases and check the characteristic difference between them. In addition, we study the nature of topological states in the case of non-trivial gapless (semi-metallic) region.