Topological origin of non-Hermitian skin effect in higher dimensions and uniform spectra

Abstract

The non-Hermitian skin effect is an iconic phenomenon characterized by the aggregation of eigenstates near the system boundaries in non-Hermitian systems. While extensively studied in one dimension, understanding the skin effect and extending the non-Bloch band theory to higher dimensions encounters a formidable challenge, primarily due to infinite lattice geometries or open boundary conditions. This work adopts a point-gap perspective and unveils that non-Hermitian skin effect in all spatial dimensions originates from point gaps. We introduce the concept of uniform spectra and reveal that regardless of lattice geometry, their energy spectra are universally given by the uniform spectra, even though their manifestations of skin modes may differ. Building on the uniform spectra, we demonstrate how to account for the skin effect with generic lattice cuts and establish the connections of skin modes across different geometric shapes via momentum-basis transformations. Our findings highlight the pivotal roles point gaps play, offering a unified understanding of the topological origin of non-Hermitian skin effect in all dimensions.

8+1 pages, 4+1 figures

References in corpus (22)

• Making Sense of Non-Hermitian Hamiltonians
• Topological Origin of Non-Hermitian Skin Effects
• Efficient Light Funneling based on the non-Hermitian Skin Effect
• Non-Hermitian Topology and Exceptional-Point Geometries
• Periodic Table for Topological Bands with Non-Hermitian Bernard-LeClair Symmetries
• Universal non-Hermitian skin effect in two and higher dimensions
• Observation of Non-Hermitian Skin Effect and Topology in Ultracold Atoms
• Non-Hermitian topological phenomena: A review
• Observation of hybrid higher-order skin-topological effect in non-Hermitian topolectrical circuits
• Observation of higher-order non-Hermitian skin effect
• Non-Hermitian Edge Burst
• Observation of Acoustic Non-Hermitian Bloch Braids and Associated Topological Phase Transitions
• Amoeba Formulation of Non-Bloch Band Theory in Arbitrary Dimensions
• Knot topology of exceptional point and non-Hermitian no-go theorem
• Exceptional Non-Abelian Topology in Multiband Non-Hermitian Systems
• Dimensional transmutation from non-Hermiticity
• Engineering Non-Hermitian Skin Effect with Band Topology in Ultracold Gases
• Observation of dynamical degeneracy splitting for the non-Hermitian skin effect
• Dynamical Degeneracy Splitting and Directional Invisibility in Non-Hermitian Systems
• Observing dynamical currents in a non-Hermitian momentum lattice
• Dynamical signatures of point-gap Weyl semimetal
• Unravelling the edge spectra of non-Hermitian Chern insulators

Cited by in corpus (27)

• Scale-tailored localization and its observation in non-Hermitian electrical circuits
• The non-Hermitian skin effect: A perspective
• Non-Hermitian Second-Order Topological Phases and Bipolar Skin Effect in Photonic Kagome Crystals
• Algebraic non-Hermitian skin effect and generalized Fermi surface formula in arbitrary dimensions
• Braiding Topology of Non-Hermitian Open-Boundary Bands
• Universal spectral moment theorem and its applications in non-Hermitian systems
• Skin Effect Induced Anomalous Dynamics from Charge-Fluctuating Initial States
• Interaction-Induced Second-Order Skin Effect
• General theory for infernal points in non-Hermitian systems
• Anisotropic-scaling localization in higher-dimensional non-Hermitian systems
• Delocalization of skin steady states
• Non-reciprocity is necessary for robust dimensional reduction and strong responses in stochastic topological systems
• Real-time edge dynamics of non-Hermitian lattices
• Tentaclelike spectra and bound states in Hatano-Nelson chain with long-range impurity coupling
• Theory for the spectral splitting exponent of exceptional points
• Unveiling Non-Hermitian Spectral Topology in Hyperbolic Lattices with Non-Abelian Translation Symmetry
• Non-Hermitian reshaping of high-order Landau modes
• Non-Hermitian Delocalization Induced by Residue Imaginary Velocity
• Experimentally Probing Non-Hermitian Spectral Transition and Eigenstate Skewness
• Concurrent Skin-scale-free Localization and Criticality under Möbius Boundary Conditions in a Non-Hermitian Ladder
• Minimal Hamiltonian deformations as bulk probes of effective non-Hermiticity in Dirac materials
• Size-Dependent Skin Effect Transitions in Weakly Coupled Non-Reciprocal Chains
• Optimal spectral transport of non-Hermitian systems
• Unified Multipole Bott Indices for Non-Hermitian Skin Effect in Different Orders
• Anatomy of Higher-Order Non-Hermitian Skin and Boundary Modes
• Wiener-Hopf factorization and non-Hermitian topology for Amoeba formulation in one-dimensional multiband systems
• Geometric origin of self-intersection points in non-Hermitian energy spectra