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In this paper, we study the topological properties of the non-HermitianSu-Schrieffer-Heeger (SSH) lattice by periodically introducing onsite imaginarypotentials in the manner of ($i\gamma_1$, $-i\gamma_2$, $-i\gamma_1$,$i\gamma_2$) where $\gamma_1$ and $\gamma_2$ are the imaginary potentialstrengths. Results show that by changing the lattice to a tetramerizednon-Hermitian system, such imaginary potentials induce the nontrivialtransition of the topological properties of the SSH system. First, thetopologically-nontrivial region is extended, followed by the non-Hermitianspontaneous breaking of the anti-$\cal PT$ symmetry. In addition, new edgestate appears, but its locality is different from the state induced by theHermitian SSH lattice. If such potentials are strong enough, the bulk states ofthis system can become purely imaginary states. We believe that these imaginarypotentials play special roles in modulating the topological properties of thenon-Hermitian SSH lattice.

Topological properties in the non-Hermitian tetramerized Su-Schrieffer-Heeger lattices