  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.

Other Condensed Matter;Quantum Physics