Non-Hermitian boundary spectral winding

Abstract

Spectral winding of complex eigenenergies represents a topological aspect unique in non-Hermitian systems, which vanishes in one-dimensional (1D) systems under the open boundary conditions (OBC). In this work, we discover a boundary spectral winding in two-dimensional non-Hermitian systems under the OBC, originating from the interplay between Hermitian boundary localization and non-Hermitian non-reciprocal pumping. Such a nontrivial boundary topology is demonstrated in a non-Hermitian breathing Kagome model with a triangle geometry, whose 1D boundary mimics a 1D non-Hermitian system under the periodic boundary conditions with nontrivial spectral winding. In a trapezoidal geometry, such a boundary spectral winding can even co-exist with corner accumulation of edge states, instead of extended ones along 1D boundary of a triangle geometry. An OBC type of hybrid skin-topological effect may also emerge in a trapezoidal geometry, provided the boundary spectral winding completely vanishes. By studying the Green's function, we unveil that the boundary spectral winding can be detected from a topological response of the system to a local driving field, offering a realistic method to extract the nontrivial boundary topology for experimental studies.

10 pages, 7 figures. Comments are welcome

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• Occupation-dependent particle separation in one-dimensional non-Hermitian lattices
• A brief review of hybrid skin-topological effect
• Non-Hermitian Topology in Hermitian Topological Matter
• Phase transitions and bunching of correlated particles in a non-Hermitian quasicrystal
• Geometry-dependent skin effect and anisotropic Bloch oscillations in a non-Hermitian optical lattice
• From Ergodicity to Many-Body Localization in a One-Dimensional Interacting Non-Hermitian Stark System
• Giant non-reciprocity and gyration through modulation-induced Hatano-Nelson coupling in integrated photonics
• Intrinsic-perturbation induced anomalous higher-order boundary states in non-Hermitian systems
• Non-reciprocity is necessary for robust dimensional reduction and strong responses in stochastic topological systems
• Anisotropic-scaling localization in higher-dimensional non-Hermitian systems
• From Complexification to Self-Similarity: New Aspects of Quantum Criticality
• Topological and fractal defect states in non-Hermitian lattices
• Tailoring Corner States and Exceptional Points in Altermagnets
• Reversing non-Hermitian skin accumulation with a non-local transverse switch