# Coexistence of non-Hermitian skin effect and extended states in one-dimensional nonreciprocal lattices

**Authors:** Han Xiao, Qi-Bo Zeng  
**arXiv:** [2403.19430](https://arxiv.org/abs/2403.19430)  
**Date:** 2024-03-28  
**Summary page:** https://www.summarizepaper.com/en/paper/2403.19430v1/

## Key points

- Han Xiao and Qi-Bo Zeng study one-dimensional non-Hermitian lattices with staggered onsite modulations and nonreciprocal hopping up to the next-nearest-neighboring (NNN) sites.
- They focus on the behavior of the system under open boundary conditions (OBC), which shows energy-dependent characteristics due to NNN nonreciprocity.
- The researchers observe NHSE edges in the eigenenergy spectrum, effectively separating eigenstates localized at opposite ends of the lattice.
- The interplay between nonreciprocal hopping and onsite modulations can lead to a reversal in the direction of the skin effect and modify the position of the NHSE edge.
- Manipulating system parameters allows certain eigenstates under OBC to transition into fully extended states with imaginary eigenenergies under both open and periodic boundary conditions, enabling coexistence of extended states alongside NHSH within the same system.
- Setting modulation parameters to be imaginary can completely dissolve , resulting in all eigenstates becoming extended.

## Summary

In their study, Han Xiao and Qi-Bo Zeng investigate the behavior of one-dimensional non-Hermitian lattices with staggered onsite modulations and nonreciprocal hopping up to the next-nearest-neighboring (NNN) sites. They focus on the  in the system under open boundary conditions (OBC), which exhibits energy-dependent characteristics due to NNN nonreciprocity. The researchers observe NHSE edges in the eigenenergy spectrum, effectively separating eigenstates localized at opposite ends of the lattice. Through their analysis, Xiao and Zeng discover that the interplay between nonreciprocal hopping and onsite modulations can lead to a reversal in the direction of the skin effect and modify the position of the NHSE edge. By manipulating system parameters, they find that certain eigenstates under OBC can transition into fully extended states with imaginary eigenenergies under both open and periodic boundary conditions. This phenomenon allows for the coexistence of extended states alongside NHSH within the same system. Furthermore, Xiao and Zeng demonstrate that by setting modulation parameters to be imaginary, it is possible to completely dissolve , resulting in all eigenstates becoming extended. This intricate interplay between onsite modulations and nonreciprocal hopping sheds light on the complex dynamics present in non-Hermitian systems.