Topological Origin of Non-Hermitian Skin Effects

Abstract

A unique feature of non-Hermitian systems is the skin effect, which is the extreme sensitivity to the boundary conditions. Here, we reveal that the skin effect originates from intrinsic non-Hermitian topology. Such a topological origin not merely explains the universal feature of the known skin effect, but also leads to new types of the skin effects---symmetry-protected skin effects. In particular, we discover the ${\mathbb{Z}}_2$ skin effect protected by time-reversal symmetry. On the basis of topological classification, we also discuss possible other skin effects in arbitrary dimensions. Our work provides a unified understanding about the bulk-boundary correspondence and the skin effects in non-Hermitian systems.

7+21 pages, 2+3 figures

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• Dislocation Non-Hermitian Skin Effect
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• Fate of fractional quantum Hall states in open quantum systems: characterization of correlated topological states for the full Liouvillian
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• Tunable two-dimensional laser arrays with zero-phase locking
• Evolution of spectral topology in one-dimensional long-range nonreciprocal lattices
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• Eigenstate clustering around exceptional points
• The Quantum Skin Hall Effect
• Machine learning of mirror skin effects in the presence of disorder
• Exact solutions of non-Hermitian chains with asymmetric long-range hopping under specific boundary conditions
• Phase Diagram of a Non-Hermitian Chern Insulator: Destabilization of Chiral Edge States and Bulk-Boundary Correspondence
• Non-Hermitian Topoelectrical Circuits: Expedient Tools for Topological State Engineering with Gain-Loss Modulation
• Band topology of pseudo-Hermitian phases through tensor Berry connections and quantum metric
• Scaling rule in critical non-Hermitian skin effect
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• Non-Hermitian Higher-Order Weyl Semimetals
• Non-Hermitian Higher-Order Dirac Semimetals
• Supermetal-insulator transition in a non-Hermitian network model
• Self-healing of non-Hermitian topological skin modes