PT-Symmetry in Non-Hermitian Su-Schrieffer-Heeger model with complex boundary potentials

TL;DR

This paper investigates the effects of non-Hermitian PT-symmetric boundary potentials on the topological phases of the SSH model, revealing phase-dependent symmetry breaking and edge state stability.

Contribution

It introduces the analysis of PT-symmetric boundary potentials in the SSH model, highlighting distinct effects on eigenvalue spectra and edge states in trivial and nontrivial phases.

Findings

In trivial phase, PT-symmetry undergoes two phase transitions as potential strength varies.

In nontrivial phase, zero-mode edge states become unstable for any nonzero imaginary potential.

The system exhibits spontaneous PT-symmetry breaking characterized by imaginary eigenmodes.

Abstract

We study the parity- and time-reversal PT symmetric non-Hermitian Su-Schrieffer-Heeger (SSH) model with two conjugated imaginary potentials $\pm i\gamma $ at two end sites. The SSH model is known as one of the simplest two-band topological models which has topologically trivial and nontrivial phases. We find that the non-Hermitian terms can lead to different effects on the properties of the eigenvalues spectrum in topologically trivial and nontrivial phases. In the topologically trivial phase, the system undergos an abrupt transition from unbroken PT-symmetry region to spontaneously broken $\mathcal{PT} $-symmetry region at a certain $\gamma_{c}$, and a second transition occurs at another transition point $\gamma_{c^{'}}$ when further increasing the strength of the imaginary potential $\gamma$. But in the topologically nontrivial phase, the zero-mode edge states become unstable for arbitrary nonzero $\gamma$ and the $\mathcal{PT}$-symmetry of the system is spontaneously broken, which is characterized by the emergence of a pair of conjugated imaginary modes.