Two-dimensional non-Hermitian topological phases induced by asymmetric hopping in a one-dimensional superlattice

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