We study the parity- and time-reversal ($\mathcal{PT}$) 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 the unbroken $\mathcal{PT}$-symmetry region to the spontaneously broken $\mathcal{PT}$-symmetry region at a certain ${\gamma }_c$, and a second transition occurs at another transition point ${\gamma }_{c^{{}^{\prime }}}$ 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.

• Received 26 March 2014

DOI:https://doi.org/10.1103/PhysRevA.89.062102