  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.
