Non-Hermitian skin effect edge

Abstract

Non-Hermitian skin effect (NHSE) is a unique phenomenon studied intensively in non-Hermitian systems during the past few years. In this work, we discuss the energy dependence of NHSE by introducing nonreciprocity beyond the nearest-neighboring hopping in the one-dimensional lattices. The direction of NHSE reverses as the eigenenergy of the system under open boundary conditions (OBCs) sweeps across some critical energies. To characterize such a phenomenon, we introduce the concept of non-Hermitian skin effect edges, which separate the eigenstates localized at opposite ends of the lattice in the OBC spectrum. We find the skin effect edges are determined by the self-intersections in the spectrum under periodic boundary conditions (PBCs), which are topological as the winding number of the PBC spectrum changes sign when crossing them. Moreover, the NHSE edges will disappear when the self-intersections merge into a single point by tuning the system parameters. Our work reveals the intricate interplay between NHSE and nonreciprocal hopping in non-Hermitian systems.

12 pages, including Appendix

References in corpus (10)

• Making Sense of Non-Hermitian Hamiltonians
• Topological Origin of Non-Hermitian Skin Effects
• Visualization of Branch Points in PT-Symmetric Waveguides
• Observation of parity-time symmetry breaking in a single spin system
• Periodic Table for Topological Bands with Non-Hermitian Bernard-LeClair Symmetries
• Defining a bulk-edge correspondence for non-Hermitian Hamiltonians via singular-value decomposition
• Localization in one dimensional lattices with non-nearest-neighbor hopping: Generalized Anderson and Aubry-André models
• Mixed-state evolution in the presence of gain and loss
• Hermitian zero modes protected by nonnormality: Application of pseudospectra
• Evolution of spectral topology in one-dimensional long-range nonreciprocal lattices

Cited by in corpus (10)

• Imaginary gap-closed points and dynamics in a class of dissipative systems
• Coexistence of non-Hermitian skin effect and extended states in one-dimensional nonreciprocal lattices
• Topological Invariant for Multi-Band Non-hermitian Systems with Chiral Symmetry
• Dual Symmetry Classification of Non-Hermitian Systems and ${\mathbb{Z}}_2$ Point-Gap Topology of a Non-Unitary Quantum Walk
• Gaussian eigenstate pinning in non-Hermitian quantum mechanics
• Size-Dependent Skin Effect Transitions in Weakly Coupled Non-Reciprocal Chains
• Edge states and persistent current in a PT-symmetric extended Su-Schrieffer-Heeger model with generic boundary conditions
• Reversing non-Hermitian skin accumulation with a non-local transverse switch
• Geometric origin of self-intersection points in non-Hermitian energy spectra
• Spread complexity and localization in $\mathcal{P}\mathcal{T}$-symmetric systems