Non-Hermitian Z4 skin effect protected by glide symmetry

Although nonsymmorphic symmetry protects Z₄ topology for Hermitian systems, non-Hermitian topological phenomena induced by such a unique topological structure remain elusive. In this paper, we elucidate that systems with glide symmetry exhibit non-Hermitian skin effects (NHSE) characterized by Z₄ topology. Specifically, numerically analyzing a two-dimensional toy model, we demonstrate that the Z₄ topology induces the NHSE when the topological invariant takes ν=1 and 2. Furthermore, our numerical analysis demonstrates that the NHSE is destroyed by perturbations preserving the relevant symmetry when the Z₄ invariant takes ν=4.