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Imaginary-Stark skin effect

Heng Lin1, Jinghui Pi1,*, Yunyao Qi1, Wei Qin2, Franco Nori3,4, and Gui-Lu Long1,5,6,†

  • *Contact author: pijh14@gmail.com
  • †Contact author: gllong@tsinghua.edu.cn
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Phys. Rev. Research 7, 033150 – Published 13 August, 2025

DOI: https://doi.org/10.1103/xc42-7hcg

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.

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Phys. Rev. Research 7, 033150– Published 13 August, 2025
  • Received 1 May 2024
  • Accepted 10 July 2025
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