Algebraic States in Continuum in $d>1$ Dimensional Non-Hermitian Systems

Abstract

We report the existence of algebraically localized eigenstates embedded within the continuum spectrum of 2D non-Hermitian systems with a single impurity. These modes, which we term algebraic states in continuum (AICs), decay algebraically as $1/|r|$ from the impurity site, and their energies lie within the bulk continuum spectrum under periodic boundary conditions. We analytically derive the threshold condition for the impurity strength required to generate such states. Remarkably, AICs are forbidden in Hermitian systems and in 1D non-Hermitian systems, making them unique to non-Hermitian systems in two and higher dimensions. To detect AICs, we introduce a local density of states as an experimental observable, which is readily accessible in photonic/acoustic platforms.

arXiv comment18 pages, 5 figures

References in corpus (49)

• Edge states and topological invariants of non-Hermitian systems
• Anderson Transitions
• Non-Hermitian Physics
• Biorthogonal Bulk-Boundary Correspondence in Non-Hermitian Systems
• Topological Origin of Non-Hermitian Skin Effects
• 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
• Observation of non-Hermitian bulk-boundary correspondence in quantum dynamics
• 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
• Non-Hermitian skin effect and chiral damping in open quantum systems
• Observation of non-Hermitian degeneracies in a chaotic exciton-polariton billiard
• Observation of non-Hermitian topology and its bulk-edge correspondence in an active mechanical metamaterial
• Topology by Dissipation in Atomic Quantum Wires
• Non-Hermitian bulk-boundary correspondence and auxiliary generalized Brillouin zone theory
• Hybrid higher-order skin-topological modes in non-reciprocal systems
• Critical non-Hermitian Skin Effect
• Universal non-Hermitian skin effect in two and higher dimensions
• Topologically protected defect states in open photonic systems with non-hermitian charge-conjugation and parity-time symmetry
• Probing non-Hermitian Skin Effect and non-Bloch Phase Transitions
• Non-Hermitian skin modes induced by on-site dissipations and chiral tunneling effect
• Quantum Oscillation from In-gap States and non-Hermitian Landau Level Problem
• Non-Bloch band theory of non-Hermitian Hamiltonians in the symplectic class
• Entanglement Phase Transition Induced by the Non-Hermitian Skin Effect
• Topological framework for directional amplification in driven-dissipative cavity arrays
• Simple formulas of directional amplification from non-Bloch band theory
• Observation of exceptional points and skin effect correspondence in non-Hermitian phononic crystals
• 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
• Dislocation Non-Hermitian Skin Effect
• Quantized classical response from spectral winding topology
• Geometric Origin of Non-Bloch PT Symmetry Breaking
• Non-Hermitian skin effect of dislocations and its topological origin
• Dynamical Degeneracy Splitting and Directional Invisibility in Non-Hermitian Systems
• Observation of dynamical degeneracy splitting for the non-Hermitian skin effect
• A non-Hermitian optical atomic mirror
• Non-Hermitian dislocation modes: Stability and melting across exceptional points
• Edge theory of non-Hermitian skin modes in higher dimensions
• Geometry-dependent skin effect and anisotropic Bloch oscillations in a non-Hermitian optical lattice
• Algebraic non-Hermitian skin effect and generalized Fermi surface formula in arbitrary dimensions
• Point-Gap Bound States in Non-Hermitian Systems
• Tailoring Bound State Geometry in High-Dimensional Non-Hermitian Systems
• Experimentally Probing Non-Hermitian Spectral Transition and Eigenstate Skewness