Effective impurity behavior emergent from non-Hermitian proximity effect

TL;DR

This paper introduces the non-Hermitian proximity effect (NHPE), revealing how non-Hermitian boundaries induce localized imaginary in-gap states with unique dynamical behaviors and physical manifestations as corner modes in open quantum systems.

Contribution

It uncovers the non-Hermitian proximity effect and its role in generating in-gap states, connecting boundary non-Hermiticity to impurity-like phenomena and corner modes.

Findings

Imaginary in-gap states are localized at boundaries and decay into the bulk.

These states exhibit distinct dynamical behaviors under time evolution.

Corner modes emerge as a manifestation of NHPE combined with NHSE.

Abstract

Non-Hermitian boundaries commonly take place in many open quantum systems locally coupled to a surrounding environment. Here, we reveal a type of non-Hermitian effect induced by non-Hermitian boundaries, the non-Hermitian proximity effect (NHPE), which describes the penetration of non-Hermiticity from the boundary into the bulk. For gapped quantum systems, the NHPE generates in-gap states with imaginary eigenenergies, termed ``imaginary in-gap states". The imaginary in-gap states are localized at the system boundary and decay into the bulk, analogous to the behaviors of the conventional impurity states. However, in contrast to impurity states, the imaginary in-gap states exhibit distinct dynamical behaviors under time-evolution. Moreover, they are physically manifested as corner modes under open boundaries, as a combined result of the non-Hermitian skin effect (NHSE) and NHPE. These results not only uncover implicit similarities between quantum systems with non-Hermitian boundaries and impurity physics, but also point to intriguing non-Hermitian phenomena broadly relevant to open quantum systems.