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

TL;DR

This paper reveals that non-Hermitian systems with glide symmetry can exhibit a $ Z_4$-protected skin effect, with the topological invariant dictating the presence or absence of the effect, supported by numerical analysis.

Contribution

It demonstrates for the first time that non-Hermitian skin effects can be protected by $ Z_4$ topology in systems with glide symmetry, extending Hermitian topological concepts to non-Hermitian physics.

Findings

The $ Z_4$ topology induces non-Hermitian skin effects for invariants $ u=1,2$.

The skin effect is destroyed by symmetry-preserving perturbations when $ u=4$.

Numerical analysis confirms the topological protection of the skin effect.

Abstract

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 $\nu=4$.