Delocalization of topological edge states

TL;DR

This paper explores the competition between non-Hermitian skin effect and topological localization in 1D systems, revealing conditions under which topological edge states become perfectly delocalized, with potential applications.

Contribution

It uncovers the phenomenon of delocalized topological edge states occurring at critical parameters, linking spectral properties to delocalization in non-Hermitian topological systems.

Findings

Topologically protected edge states can be perfectly delocalized at critical points.

Delocalization occurs when edge state spectra align with the system's complex spectral loop.

Numerical simulations confirm the reconstructability of delocalized edge states from time evolution.

Abstract

The non-Hermitian skin effect (NHSE) in non-Hermitian lattice systems depicts the exponential localization of eigenstates at system's boundaries. It has led to a number of counter-intuitive phenomena and challenged our understanding of bulk-boundary correspondence in topological systems. This work aims to investigate how the NHSE localization and topological localization of in-gap edge states compete with each other, with several representative static and periodically driven 1D models, whose topological properties are protected by different symmetries. The emerging insight is that at critical system parameters, even topologically protected edge states can be perfectly delocalized. In particular, it is discovered that this intriguing delocalization occurs if the real spectrum of the system's edge states falls on the same system's complex spectral loop obtained under the periodic boundary condition. We have also performed sample numerical simulation to show that such delocalized topological edge states can be safely reconstructed from time-evolving states. Possible applications of delocalized topological edge states are also briefly discussed.