Non-Hermitian Topological Invariants in Real Space

Abstract

The topology of non-Hermitian systems is drastically shaped by the non-Hermitian skin effect, which leads to the generalized bulk-boundary correspondence and non-Bloch band theory. The essential part in formulations of bulk-boundary correspondence is a general and computable definition of topological invariants. In this paper, we introduce a construction of non-Hermitian topological invariants based directly on real-space wavefunctions, which provides a general and straightforward approach for determining non-Hermitian topology. As an illustration, we apply this formulation to several representative models of non-Hermitian systems, efficiently obtaining their topological invariants in the presence of non-Hermitian skin effect. Our formulation also provides a dual picture of the non-Bloch band theory based on the generalized Brillouin zone, offering a unique perspective of bulk-boundary correspondence.

arXiv comment6 pages, 3 figures; PRL Editors' Suggestion

References in corpus (92)

• Anyons in an exactly solved model and beyond
• Topological Photonics
• Edge states and topological invariants of non-Hermitian systems
• Localization transitions in non-Hermitian quantum mechanics
• Topological phases of non-Hermitian systems
• Symmetry and Topology in Non-Hermitian Physics
• Biorthogonal Bulk-Boundary Correspondence in Non-Hermitian Systems
• Topological Band Theory for Non-Hermitian Hamiltonians
• Anomalous edge state in a non-Hermitian lattice
• Non-Bloch Band Theory of Non-Hermitian Systems
• Non-Hermitian Chern bands
• Spawning rings of exceptional points out of Dirac cones
• 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
• Edge Modes, Degeneracies, and Topological Numbers in Non-Hermitian Systems
• Probing topological invariants in the bulk of a non-Hermitian optical system
• Observation of Bulk Fermi Arc and Polarization Half Charge from Paired Exceptional Points
• Non-Hermitian skin effect and chiral damping in open quantum systems
• Selective enhancement of topologically induced interface states in a dielectric resonator chain
• Topology by Dissipation in Atomic Quantum Wires
• Topological phases in the non-Hermitian Su-Schrieffer-Heeger model
• Weyl Exceptional Rings in a Three-Dimensional Dissipative Cold Atomic Gas
• 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
• Topological Transition in a Non-Hermitian Quantum Walk
• Periodic Table for Topological Bands with Non-Hermitian Bernard-LeClair Symmetries
• Classification of Exceptional Points and Non-Hermitian Topological Semimetals
• Topologically protected defect states in open photonic systems with non-hermitian charge-conjugation and parity-time symmetry
• 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
• Interplay of non-Hermitian skin effects and Anderson localization in non-reciprocal quasiperiodic lattices
• New topological invariants in non-Hermitian systems
• Experimental realization of a Weyl exceptional ring
• Mapping topological order in coordinate space
• Higher-order topological corner states induced by gain and loss
• Entanglement Spectrum of a Disordered Topological Chern Insulator
• Topological states of non-Hermitian systems
• Non-Hermitian perspective of the band structure in heavy-fermion systems
• Topological unification of time-reversal and particle-hole symmetries in non-Hermitian physics
• Exceptional rings in two-dimensional correlated systems with chiral symmetry
• Majorana bound states from exceptional points in non-topological superconductors
• PT-Symmetry in Non-Hermitian Su-Schrieffer-Heeger model with complex boundary potentials
• Quantum Oscillation from In-gap States and non-Hermitian Landau Level Problem
• Non-Hermitian extensions of higher-order topological phases and their biorthogonal bulk-boundary correspondence
• Symmetry-protected nodal phases in non-Hermitian systems
• Theory of Non-Hermitian Fermionic Superfluidity with a Complex-Valued Interaction
• Topological exceptional surfaces in non-Hermitian systems with parity-time and parity-particle-hole symmetries
• Defining a bulk-edge correspondence for non-Hermitian Hamiltonians via singular-value decomposition
• Detecting topological invariants in nonunitary discrete-time quantum walks
• Non-Hermitian systems and topology: A transfer-matrix perspective
• Phase-dependent chiral transport and effective non-Hermitian dynamics in a bosonic Kitaev-Majorana chain
• Flat Band in Disorder Driven Non-Hermitian Weyl Semimetals
• Exceptional Surfaces in PT-Symmetric Photonic Systems
• Non-Bloch topological invariants in a non-Hermitian domain-wall system
• Non-Hermitian Hopf-Link Exceptional Line Semimetals
• Parity-time-symmetric topological superconductor
• Non-Hermitian higher-order topological states in nonreciprocal and reciprocal systems with their electric-circuit realization
• Exceptional Links and Twisted Fermi Ribbons in non-Hermitian Systems
• Non-Hermitian nodal-line semimetals with an anomalous bulk-boundary correspondence
• Effects of non-Hermitian perturbations on Weyl Hamiltonians with arbitrary topological charges
• Non-Hermitian topology: a unifying framework for the Andreev versus Majorana states controversy
• Non-Hermitian boundary and interface states in nonreciprocal higher-order topological metals and electrical circuits
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• Nodal Arc in Disordered Dirac Fermions: Connection to Non-Hermitian Band Theory
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• Non-Hermitian Floquet topological phases with arbitrarily many real-quasienergy edge states
• Topological invariants and phase diagrams for one-dimensional two-band non-Hermitian systems without chiral symmetry
• Relation between $\mathcal{P}\mathcal{T}$-symmetry breaking and topologically nontrivial phases in the SSH and Kitaev models
• Non-Hermitian gauged topological laser arrays
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• Non-Quantized Edge Channel Conductance and Zero Conductance Fluctuation in Non-Hermitian Chern Insulators
• Topological Landau Lattice

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