Non-Hermitian systems can host topological states with unusual topological invariants and bulk-edge correspondences that are distinct from conventional Hermitian systems. Here we show that two unique classes of non-Hermitian two-dimensional topological phases, a $2\mathbb{Z}$ non-Hermitian Chern insulator and a ${\mathbb{Z}}_2$ topological semimetal, can be realized by solely tuning staggered non-Hermitian or asymmetric hopping strengths in a one-dimensional (1D) superlattice. These non-Hermitian topological phases support real edge modes due to robust $\mathcal{PT}$-symmetric-like spectra and can coexist in a certain parameter regime. The proposed phases can be experimentally realized in photonic or atomic systems and may open an avenue for exploring unique classes of non-Hermitian topological phases with 1D superlattices.

• Received 14 May 2020
• Revised 7 January 2021
• Accepted 28 January 2021

DOI:https://doi.org/10.1103/PhysRevA.103.033305