Interplay between defects and the non-Hermitian skin effect

TL;DR

This paper explores how defects influence the non-Hermitian skin effect in one-dimensional lattices, revealing size-dependent hybrid states and topological transitions driven by defect strength and system boundaries.

Contribution

It introduces a new class of hybrid skin-defect states and analyzes the interplay between topological defect states and the NHSE in non-reciprocal systems.

Findings

Hybrid skin-defect states depend on system size.

Transition from topologically nontrivial defect states to skin states.

Decreasing defect strength induces a transition to skin states.

Abstract

The non-Hermitian skin effect (NHSE) is an intriguing phenomenon in which an extensive number of bulk eigenstates localize at the boundaries of a non-Hermitian system with non-reciprocal hoppings. Here we study the interplay of this effect and a defect in non-reciprocal one-dimensional lattices. We show that the interplay of the NHSE and defects is size-dependent. We demonstrate a novel class of hybrid skin-defect states in finite-size systems resulting from the coupling between the skin and defect states. Next, we consider a single defect in a topologically nontrivial lattice with time-reversal symmetry based on the non-reciprocal Su-Schrieffer-Heeger configuration. We unveil how topologically nontrivial defect states and non-Hermiticity interplay by competing with each other, exhibiting a transition from topologically nontrivial defect states to skin states. In addition, we show that decreasing the defect strength can result in a transition from trivial defect states to skin states. Our work promotes the understanding of the interplay between defects and the NHSE, and especially the importance of the energy spectra of the system with the defect under periodic boundary conditions.