Imaginary-Stark Skin Effect

TL;DR

This paper introduces the imaginary-Stark skin effect (ISSE), a novel non-Hermitian skin effect in lossy lattices with spatially increasing loss, revealing unique spectral and localization properties beyond existing theories.

Contribution

It uncovers the ISSE phenomenon in non-translational invariant systems, expanding understanding of non-Hermitian skin effects beyond non-Bloch band theory.

Findings

Energy spectrum exhibits a T-shaped feature.

Approximately half of the eigenstates localize at the boundary.

Skin modes are stable, exponentially-decaying waves.

Abstract

A unique phenomenon in non-Hermitian systems is the non-Hermitian skin effect (NHSE), namely the boundary localization of continuous-spectrum eigenstates. However, studies on the NHSE in systems without translational invariance are still limited. Here, we unveil a new class of NHSE, dubbed the imaginary-Stark skin effect (ISSE), in a one-dimensional lossy lattice with a spatially increasing loss rate. This ISSE is beyond the framework of non-Bloch band theory and exhibits intriguing properties significantly different from the conventional NHSE. Specifically, the energy spectrum of our model has a T-shaped feature, with approximately half of the eigenstates localized at the left boundary. Furthermore, each skin mode can be expressed as a single stable, exponentially-decaying wave within the bulk region. Such peculiar behaviors are analyzed via the transfer-matrix method, whose eigendecomposition quantifies the formation of the ISSE. Our work provides new insights into the NHSE in systems without translational symmetry and contributes to the understanding of non-Hermitian systems.