Parsing skin effect in a non-Hermitian spinless BHZ-like model

Abstract

This work comprehensively investigates the non-Hermitian skin effect (NHSE) in a spinless Bernevig- Hughes-Zhang (BHZ)-like model in one dimension. It is generally believed that a system with non-reciprocal hopping amplitudes demonstrates NHSE. However, we show that there are exceptions, and more in-depth analyses are required to decode the presence of NHSE or its variants in a system. The fascinating aspects of our findings, depending on the inclusion of non-reciprocity in the inter-orbital hopping terms, concede the existence of conventional NHSE or NHSE at both edges and even a surprising absence of NHSE. The topological properties and the (bi-orthogonal) bulk-boundary correspondence, enumerated via computation of the (complex) Berry phase and spatial localization of the edge modes, highlight the topological phase transitions occurring therein. Further, to facilitate a structured discussion of the non-Hermitian model, we split the results into PT symmetric and non-PT symmetric cases with a view to comparing the two.

arXiv commentAccepted in Journal of Physics: Condensed Matter; 14 pages, 15 figures, and 1 table

References in corpus (49)

• Topological Insulators
• Topological insulators and superconductors
• Quantum Spin Hall Effect in Graphene
• Quantum Spin Hall Effect and Topological Phase Transition in HgTe Quantum Wells
• Real Spectra in Non-Hermitian Hamiltonians Having PT Symmetry
• $Z_2$ Topological Order and the Quantum Spin Hall Effect
• Topological Insulators in Three Dimensions
• Classification of topological insulators and superconductors in three spatial dimensions
• Classification of topological quantum matter with symmetries
• Novel Symmetry Classes in Mesoscopic Normal-Superconducting Hybrid Structures
• Topological insulators and superconductors: ten-fold way and dimensional hierarchy
• Edge states and topological invariants of non-Hermitian systems
• Complex Extension of Quantum Mechanics
• Exceptional Topology of Non-Hermitian Systems
• Non-Hermitian Physics
• Pseudo-Hermiticity versus PT Symmetry: The necessary condition for the reality of the spectrum of a non-Hermitian Hamiltonian
• Localization transitions in non-Hermitian quantum mechanics
• Topological phases of non-Hermitian systems
• The physics of exceptional points
• PT-Symmetric Quantum Mechanics
• Symmetry and Topology in 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
• Observation of bulk boundary correspondence breakdown in topolectrical circuits
• Non-Hermitian Boundary Modes
• Observation of non-Hermitian bulk-boundary correspondence in quantum dynamics
• Topological Defects and Gapless Modes in Insulators and Superconductors
• Non-Hermitian robust edge states in one-dimension: Anomalous localization and eigenspace condensation at exceptional points
• Topological phases in the non-Hermitian Su-Schrieffer-Heeger model
• Edge states and topological phases in non-Hermitian systems
• Quantum exceptional points of non-Hermitian Hamiltonians and Liouvillians: The effects of quantum jumps
• Bulk-Boundary Correspondence in a Non-Hermitian System in One Dimension with Chiral-Inversion Symmetry
• Geometrical meaning of winding number and its characterization of topological phases in one-dimensional chiral non-Hermitian systems
• Higher-order non-Hermitian skin effect
• New topological invariants in non-Hermitian systems
• Acoustic non-Hermitian skin effect from twisted winding topology
• Physical Aspects of Pseudo-Hermitian and $PT$-Symmetric Quantum Mechanics
• Non-Hermitian extensions of higher-order topological phases and their biorthogonal bulk-boundary correspondence
• Observation of critical phenomena in parity-time-symmetric quantum dynamics
• Topological defect engineering and PT-symmetry in non-Hermitian electrical circuits
• Sensitivity of parameter estimation near the exceptional point of a non-Hermitian system
• Winding Numbers, Complex Currents, and Non-Hermitian Localization
• Properties of the non-Hermitian SSH model: role of PT-symmetry
• A New Class of Adiabatic Cyclic States and Geometric Phases for Non-Hermitian Hamiltonians
• Non-Hermitian anomalous skin effect
• Exceptional points in quantum and classical dynamics
• Symmetric non-Hermitian skin effect with emergent nonlocal correspondence
• Constraints of internal symmetry on the non-Hermitian skin effect and bidirectional skin effect under the action of the Hermitian conjugate of time-reversal symmetry

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