Real spectra and phase transition of skin effect in nonreciprocal systems

TL;DR

This paper explores the spectral properties and phase transitions of the non-Hermitian skin effect in one-dimensional nonreciprocal lattices with real hopping, revealing real, imaginary, and complex energy spectra and phase-dependent skin effects.

Contribution

It introduces a detailed analysis of spectral transitions and skin effect phase changes in mosaic nonreciprocal lattices, with analytical determination of critical boundaries.

Findings

Spectra can be entirely real or imaginary under open boundary conditions.

Eigenenergies undergo real-complex-imaginary transitions as nonreciprocity varies.

Skin effect exhibits phase transitions depending on the mosaic period.

Abstract

We study the one-dimensional nonreciprocal lattices with real nearest neighboring hopping and find that the energy spectra under open boundary conditions can be entirely real or imaginary. We further investigate the spectral properties and the non-Hermitian skin effect in the one-dimensional mosaic lattices with real nonreciprocal hopping introduced at equally spaced sites. The eigenenergies of such lattices undergo a real-complex-imaginary or real-complex transition as the nonreciprocity varies. Moreover, the skin effect exhibits phase transitions depending on the period of the mosaic nonreciprocity. The bulk states are abruptly shifted from one end of the lattice to the opposite one by crossing the critical points, accompanied by the closing and reopening of point gaps in the spectra under periodic boundary conditions. The phase diagrams of the transition are presented and the critical boundaries are analytically determined. Our work unveils the intriguing properties of the energy spectrum and skin effect in non-Hermitian systems.