Topological non-Hermitian skin effect

This article reviews recent developments in the non-Hermitian skin effect (NHSE), particularly on its rich interplay with topology. The review starts off with a pedagogical introduction on the modified bulk-boundary correspondence, the synergy and hybridization of NHSE and band topology in higher dimensions, as well as, the associated topology on the complex energy plane such as spectral winding topology and spectral graph topology. Following which, emerging topics are introduced such as non-Hermitian criticality, dynamical NHSE phenomena, and the manifestation of NHSE beyond the traditional linear non-interacting crystal lattices, particularly its interplay with quantum many-body interactions. Finally, we survey the recent demonstrations and experimental proposals of NHSE.

Automated summary

This article reviews recent developments in the non-Hermitian skin effect (NHSE), particularly focusing on its interactions with topology. It starts with an introduction to the modified bulk-boundary correspondence, the synergy between NHSE and band topology in higher dimensions, and the associated topology on the complex energy plane. It then explores emerging topics such as non-Hermitian criticality, dynamical NHSE phenomena, and the manifestation of NHSE beyond linear non-interacting crystal lattices, including its interplay with quantum many-body interactions. Finally, it surveys recent demonstrations and experimental proposals of NHSE.