Abstract
We investigate the boundary condition dependence of non-Hermitian topological systems. We consider a complex extension of the Su-Schrieffer-Heeger model. We discuss that topological zero-energy modes exist if the system has open edges. We show that robust zero-energy states appear for the closed lattice too. We also consider a complex extension of the Bernevig-Hughes-Zhang Hamiltonian. We show that the translationally invariant system has a complex-valued band structure. We discuss that $\mathcal{PT}$ symmetry is restored for helical edge states if the translational invariance is lost in one direction.
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