Algebraic non-Hermitian skin effect and generalized Fermi surface formula in arbitrary dimensions

Abstract

The non-Hermitian skin effect, characterized by a proliferation of exponentially localized edge modes in open-boundary systems, has led to the discovery of numerous novel physical phenomena that challenge the limits of conventional band theory. In sharp contrast to this familiar exponential localization, we report a distinct phenomenon--the algebraic non-Hermitian skin effect--which arises generically in non-Hermitian systems with two or more spatial dimensions. In such cases, the amplitude of skin modes typically decays from the boundary following a power law, rather than an exponential form--a behavior not captured by existing theoretical frameworks. To bridge this gap and describe the transition in localization from one to higher dimensions, we develop a generalized Fermi surface framework applicable to open-boundary systems in arbitrary dimensions. This framework not only reproduces known results for the exponential skin effect in 1D, but also predicts a new class of skin effects with algebraic decay in 2D and above. We demonstrate this framework in both tight-binding and continuum models in two and three dimensions. This investigation not only unveils a novel category of the non-Hermitian skin effect but also offers a comprehensive theoretical structure that describes skin effects in any non-Hermitian system, irrespective of its spatial dimensionality.

30 pages, 13 figures

References in corpus (90)

• Classification of topological quantum matter with symmetries
• Edge states and topological invariants of non-Hermitian systems
• Exceptional Topology of Non-Hermitian Systems
• Non-Hermitian Physics
• Topological phases of non-Hermitian systems
• Symmetry and Topology in Non-Hermitian Physics
• Biorthogonal Bulk-Boundary Correspondence in Non-Hermitian Systems
• Topological Origin of Non-Hermitian Skin Effects
• Topological Band Theory for Non-Hermitian Hamiltonians
• Anomalous edge state in a non-Hermitian lattice
• Non-Bloch Band Theory of Non-Hermitian Systems
• Correspondence between winding numbers and skin modes in non-hermitian systems
• Non-Hermitian Chern bands
• Observation of bulk boundary correspondence breakdown in topolectrical circuits
• Non-Hermitian Boundary Modes
• Spawning rings of exceptional points out of Dirac cones
• Observation of non-Hermitian bulk-boundary correspondence in quantum dynamics
• Efficient Light Funneling based on the non-Hermitian Skin Effect
• Anatomy of skin modes and topology in non-Hermitian systems
• Non-Hermitian robust edge states in one-dimension: Anomalous localization and eigenspace condensation at exceptional points
• Observation of Bulk Fermi Arc and Polarization Half Charge from Paired Exceptional Points
• Non-Hermitian skin effect and chiral damping in open quantum systems
• Non-Hermitian Topology and Exceptional-Point Geometries
• Observation of non-Hermitian topology and its bulk-edge correspondence in an active mechanical metamaterial
• Non-Hermitian bulk-boundary correspondence and auxiliary generalized Brillouin zone theory
• Biorthogonal Quantum Mechanics
• Edge states and topological phases in non-Hermitian systems
• Hybrid higher-order skin-topological modes in non-reciprocal systems
• Second-Order Topological Phases in Non-Hermitian Systems
• Critical non-Hermitian Skin Effect
• Universal non-Hermitian skin effect in two and higher dimensions
• Non-Hermitian Topological Sensors
• 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
• Topological active matter
• Probing non-Hermitian Skin Effect and non-Bloch Phase Transitions
• Higher-order non-Hermitian skin effect
• Acoustic non-Hermitian skin effect from twisted winding topology
• Experimental realization of a Weyl exceptional ring
• Observation of higher-order non-Hermitian skin effect
• Odd elasticity
• Topological Non-Hermitian skin effect
• Non-Hermitian skin modes induced by on-site dissipations and chiral tunneling effect
• Topology-Induced Spontaneous Non-reciprocal Pumping in Cold-Atom Systems with Loss
• Robust light transport in non-Hermitian photonic lattices
• Non-Hermitian Morphing of Topological Modes
• Exponentially-enhanced quantum sensing with non-Hermitian lattice dynamics
• Isostaticity, auxetic response, surface modes, and conformal invariance in twisted kagome lattices
• Non-Bloch band theory of non-Hermitian Hamiltonians in the symplectic class
• Entanglement Phase Transition Induced by the Non-Hermitian Skin Effect
• Non-Hermitian systems and topology: A transfer-matrix perspective
• Phase-dependent chiral transport and effective non-Hermitian dynamics in a bosonic Kitaev-Majorana chain
• Liouvillian Skin Effect: Slowing Down of Relaxation Processes without Gap Closing
• Topological Correspondence between Hermitian and Non-Hermitian Systems: Anomalous Dynamics
• Non-Hermitian band topology and skin modes in active elastic media
• Non-Bloch topological invariants in a non-Hermitian domain-wall system
• Transient non-Hermitian skin effect
• Skin effect and winding number in disordered non-Hermitian systems
• Non-Hermitian Edge Burst
• Simple formulas of directional amplification from non-Bloch band theory
• Impurity induced scale-free localization
• Observation of exceptional points and skin effect correspondence in non-Hermitian phononic crystals
• Helical damping and anomalous critical non-Hermitian skin effect
• DMFT reveals the non-Hermitian topology in heavy-fermion systems
• Amoeba Formulation of Non-Bloch Band Theory in Arbitrary Dimensions
• Two-dimensional non-Hermitian skin effect in an ultracold Fermi gas
• Experimental Realization of Geometry-Dependent Skin Effect in a Reciprocal Two-Dimensional Lattice
• Of Bulk and Boundaries: Generalized Transfer Matrices for Tight-Binding Models
• Quantized classical response from spectral winding topology
• Enhancement of Second-Order Non-Hermitian Skin Effect by Magnetic Fields
• Active viscoelasticity of odd materials
• Non-Bloch bands in two-dimensional non-Hermitian systems
• Dimensional transmutation from non-Hermiticity
• Non-Hermitian Topological Metamaterials with Odd Elasticity
• Dynamical Degeneracy Splitting and Directional Invisibility in Non-Hermitian Systems
• Observation of dynamical degeneracy splitting for the non-Hermitian skin effect
• Designing non-Hermitian real spectra through electrostatics
• A non-Hermitian optical atomic mirror
• Observation of non-Hermitian topology in a multi-terminal quantum Hall device
• Topological origin of non-Hermitian skin effect in higher dimensions and uniform spectra
• Geometry-dependent skin effects in reciprocal photonic crystals
• Anomalous Behaviors of Quantum Emitters in Non-Hermitian Baths
• Exponentially-enhanced Quantum Non-Hermitian Sensing via Optimized Coherent Drive
• Edge theory of non-Hermitian skin modes in higher dimensions
• Non-Bloch band theory for non-Hermitian continuum systems
• Geometry-dependent skin effect and anisotropic Bloch oscillations in a non-Hermitian optical lattice
• Symmetric non-Hermitian skin effect with emergent nonlocal correspondence
• Point-Gap Bound States in Non-Hermitian Systems
• Universal spectral moment theorem and its applications in non-Hermitian systems

Cited by in corpus (4)

• Hopf Bifurcation of Nonlinear Non-Hermitian Skin Effect
• Anisotropic-scaling localization in higher-dimensional non-Hermitian systems
• Wiener-Hopf factorization and non-Hermitian topology for Amoeba formulation in one-dimensional multiband systems
• Algebraic States in Continuum in $d>1$ Dimensional Non-Hermitian Systems