The non-Hermitian skin effect: A perspective

Abstract: The non-Hermitian (NH) skin effect is a truly NH feature, which manifests itself as an accumulation of states, known as skin states, on the boundaries of a system. In this perspective, we discuss several aspects of the NH skin effect focusing on the most interesting facets of this phenomenon. Beyond reviewing necessary requirements to see the NH skin effect, we discuss the NH skin effect as a topological effect that can be seen as a manifestation of a truly NH bulk-boundary correspondence, stemming from the spectral topology, and show how skin states can be distinguished from topological boundary states. As most theoretical work has focused on studying the NH skin effect in one-dimensional non-interacting systems, recent developments of studying this effect in higher dimensions as well as in many-body systems are highlighted. Lastly, experimental signatures and applications are discussed, and an outlook is provided.