Tentaclelike spectra and bound states in Hatano-Nelson chain with long-range impurity coupling

Abstract

In non-Hermitian systems, the energy spectra and eigenstates exhibit high sensitivity to boundary conditions, lattice geometries, and local impurities. In this paper, we study the effect of long-range impurity coupling, located far from the boundaries, on the paradigmatic non-Hermitian Hatano-Nelson model. Through exact analytical treatment, we reveal the intriguing tentacle-like spectral structures that emerge from the otherwise Bloch or non-Bloch spectra under periodic or open boundary conditions, respectively. We show that these spectral tentacles are associated with emergent bound states near the impurity, with their number determined by the coupling range. We further determine the localization length of these tentacled states using the transfer matrix. Our work indicates that the long-range impurity coupling cannot be treated as a mere perturbative effect and holds promise for state manipulations in non-Hermitian systems.

References in corpus (46)

• Making Sense of Non-Hermitian Hamiltonians
• Nonreciprocal light transmission in parity-time-symmetric whispering-gallery microcavities
• Edge states and topological invariants of non-Hermitian systems
• Unidirectional Invisibility induced by PT-Symmetric Periodic Structures
• Exceptional Topology of Non-Hermitian Systems
• Non-Hermitian Physics
• Localization transitions in non-Hermitian quantum mechanics
• Biorthogonal Bulk-Boundary Correspondence in Non-Hermitian Systems
• Topological Origin of Non-Hermitian Skin Effects
• 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
• 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
• Topolectrical circuits
• 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
• Critical non-Hermitian Skin Effect
• Universal non-Hermitian skin effect in two and higher dimensions
• Non-Hermitian Topological Sensors
• Reciprocal skin effect and its realization in a topolectrical circuit
• Observation of Non-Hermitian Skin Effect and Topology in Ultracold Atoms
• Observation of hybrid higher-order skin-topological effect in non-Hermitian topolectrical circuits
• Acoustic non-Hermitian skin effect from twisted winding topology
• Non-Hermitian skin modes induced by on-site dissipations and chiral tunneling effect
• Topological Non-Hermitian skin effect
• Exact solution of non-Hermitian systems with generalized boundary conditions: size-dependent boundary effect and fragility of skin effect
• Non-Bloch band theory of non-Hermitian Hamiltonians in the symplectic class
• Knots and Non-Hermitian Bloch Bands
• Topological defect engineering and PT-symmetry in non-Hermitian electrical circuits
• Non-Bloch topological invariants in a non-Hermitian domain-wall system
• Observation of non-Hermitian topological Anderson insulator in quantum dynamics
• Skin effect and winding number in disordered non-Hermitian systems
• Impurity induced scale-free localization
• Observation of exceptional points and skin effect correspondence in non-Hermitian phononic crystals
• Accumulation of scale-free localized states induced by local non-Hermiticity
• Non-Hermitian Chiral Skin Effect
• Scale-free localization and PT symmetry breaking from local non-Hermiticity
• Zoology of non-Hermitian spectra and their graph topology
• Phase Transitions and Generalized Biorthogonal Polarization in Non-Hermitian Systems
• Topological origin of non-Hermitian skin effect in higher dimensions and uniform spectra
• Scale-tailored localization and its observation in non-Hermitian electrical circuits
• Edge theory of non-Hermitian skin modes in higher dimensions