Abstract
The topological property and the energy property of one-dimensional non-Hermitian spin-orbit-coupled Su-Schrieffer-Heeger (SSH) model are investigated theoretically, by introducing spin-dependent imaginary potentials with gain and loss effects. It is found that the imaginary potential leads the imaginary energy spectra to appera in the topologically nontrivial region of this system, and the <inline-formula><tex-math id="M5">\begin{document}${\cal {PT}}$\end{document}</tex-math><alternatives><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="17-20220796_M5.jpg"/><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="17-20220796_M5.png"/></alternatives></inline-formula> phase transition to happen in the topologically trivial region. In addition, the imaginary potential energy and spin-orbit coupling work together to make the topological phase transition occur in the topologically trivial region, and the topological non-trivial region becomes wider. The energy spectrum results show that the imaginary potential energy and the spin-orbit coupling can obviously control the zero-energy states of the system, which mainly lies in the presence of four zero-energy states with four different localities and numbers. This shows the special adjustment effect of imaginary potential energy and spin-orbit coupling on the energy band structure of the system. It is believed that these results are helpful in understanding the topological phase transition behavior of <inline-formula><tex-math id="M6">\begin{document}${\cal {PT}}$\end{document}</tex-math><alternatives><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="17-20220796_M6.jpg"/><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="17-20220796_M6.png"/></alternatives></inline-formula>-symmetric non-Hermitian system.
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