Non-Hermitian ${\mathbb{Z}}_4$ skin effect protected by glide symmetry

Although nonsymmorphic symmetry protects ${\mathbb{Z}}_4$ 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 ${\mathbb{Z}}_4$ topology. Specifically, numerically analyzing a two-dimensional toy model, we demonstrate that the ${\mathbb{Z}}_4$ topology induces the NHSE when the topological invariant takes $\nu =1,2$. Furthermore, our numerical analysis demonstrates that the NHSE is destroyed by perturbations preserving the relevant symmetry when the ${\mathbb{Z}}_4$-invariant takes $\nu =4$.