Coexistence of extended and localized states in one-dimensional non-Hermitian Anderson model

TL;DR

This paper investigates how nonreciprocal non-Hermitian one-dimensional lattices can exhibit coexistence of extended and localized states, revealing mobility edges influenced by boundary conditions and topological properties.

Contribution

It demonstrates the emergence of mobility edges in non-Hermitian lattices with or without disorder, highlighting the role of nonreciprocity and topology in state localization.

Findings

Mobility edges appear due to boundary condition sensitivity.

Extended and localized states coexist in non-Hermitian topological regions.

Boundary conditions critically influence state localization in the model.

Abstract

In one-dimensional Hermitian tight-binding models, mobility edges separating extended and localized states can appear in the presence of properly engineered quasi-periodical potentials and coupling constants. On the other hand, mobility edges don't exist in a one-dimensional Anderson lattice since localization occurs whenever a diagonal disorder through random numbers is introduced. Here, we consider a nonreciprocal non-Hermitian lattice and show that the coexistence of extended and localized states appears with or without diagonal disorder in the topologically nontrivial region. We discuss that the mobility edges appear basically due to the boundary condition sensitivity of the nonreciprocal non-Hermitian lattice.