Unified Multipole Bott Indices for Non-Hermitian Skin Effect in Different Orders

• URL: http://arxiv.org/abs/2504.12017v1
• Date: Wed, 16 Apr 2025 12:17:42 GMT
• Title: Unified Multipole Bott Indices for Non-Hermitian Skin Effect in Different Orders
• Authors: Wuping Yang, H. Huang,
• Abstract summary: We develop a set of non-Hermitian multipole Bott indices capable of diagnosing skin effects of different orders.<n>Our approach provides a comprehensive understanding of both first- and higher-order skin effects in non-Hermitian systems.
• Score: 0.0
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: Non-Hermitian systems exhibit a distinctive phenomenon known as the non-Hermitian skin effect, where an extensive number of eigenstates become localized at the boundaries of a lattice with open boundaries. While the spectral winding number under periodic boundary conditions is a well-established topological indicator for predicting the skin effect in one-dimensional non-Hermitian systems, a suitable topological invariant to diagnose higher-order skin effects remains elusive. In this Letter, we propose a unified non-Hermitian multipole characterization framework that generalizes the concept of spectral winding to higher-order skin effects. Specifically, we develop a set of non-Hermitian multipole Bott indices capable of diagnosing skin effects of different orders. Our approach provides a comprehensive understanding of both first- and higher-order skin effects in non-Hermitian systems, offering new perspectives for exploring topological phenomena in non-Hermitian systems.

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