Non-Hermitian pseudo mobility edge in a coupled chain system

TL;DR

This paper investigates how coupling a non-Hermitian skin localized chain with a delocalized chain can induce a pseudo mobility edge and explores the topological implications of these effects under various boundary conditions.

Contribution

It reveals the emergence of a pseudo mobility edge due to non-Hermitian skin effects and establishes a bulk-defect correspondence in a coupled chain system.

Findings

Non-Hermitian skin localization induces a pseudo mobility edge in the complex energy plane.

The transition from pseudo mobility edge to extended phases can be characterized by a quantized winding number.

The system exhibits a bulk-defect correspondence linking topological invariants to localized modes.

Abstract

In this work, we explore interesting consequences arising from the coupling between a clean non-Hermitian chain with skin localization and a delocalized chain of the same length under various boundary conditions (BCs). We reveal that in the ladder with weak rung coupling, the nonHermitian skin localization could induce a pseudo mobility edge in the complex energy plane, which separates states with extended and localized profiles yet allowing unidirectional transport of signals. We also demonstrate the gradual takeover of the non-Hermitian skin effect in the entire system with the increase of the rung coupling under conventional open BC. When taking open BC for the nonHermitian chain and periodic BC for the other, it is discovered that a quantized winding number defined under periodic BC could characterize the transition from the pseudo mobility edge to the trivial extended phases, establishing a "bulk-defect correspondence" in our quasi-1D non-Hermitian system. This work hence unveils more subtle properties of non-Hermitian skin effects and sheds light on the topological nature of the non-Hermitian localized modes in the proximity to systems with dissimilar localization properties.