Bulk-boundary correspondence in non-Hermitian systems: stability analysis for generalized boundary conditions

Abstract

The bulk-boundary correspondence (BBC), i.e. the direct relation between bulk topological invariants defined for infinite periodic systems and the occurrence of protected zero-energy surface states in finite samples, is a ubiquitous and widely observed phenomenon in topological matter. In non-Hermitian generalizations of topological systems, however, this fundamental correspondence has recently been found to be qualitatively altered, largely owing to the sensitivity of non-Hermitian eigenspectra to changing the boundary conditions. In this work, we report on two contributions towards comprehensively explaining this remarkable behavior unique to non-Hermitian systems with theory. First, we analytically solve paradigmatic non-Hermitian topological models for their zero-energy modes in the presence of generalized boundary conditions interpolating between open and periodic boundary conditions, thus explicitly following the breakdown of the conventional BBC. Second, addressing the aforementioned spectral fragility of non-Hermitian matrices, we investigate as to what extent the modified non-Hermitian BBC represents a robust and generically observable phenomenon.

arXiv commentInvited contribution to EPJD topical issue "Topological Ultracold Atoms and Photonic Systems". Final version

References in corpus (46)

• Topological Insulators
• Edge states and topological invariants of non-Hermitian systems
• Localization transitions in non-Hermitian quantum mechanics
• 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
• Anatomy of skin modes and topology in non-Hermitian systems
• Topological mechanics of gyroscopic metamaterials
• 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
• Topological phases in the non-Hermitian Su-Schrieffer-Heeger model
• Biorthogonal Quantum Mechanics
• Edge states and topological phases in non-Hermitian systems
• Hybrid higher-order skin-topological modes in non-reciprocal systems
• Non-reciprocal robotic metamaterials
• Non-Hermitian Topological Invariants in Real Space
• Topological negative refraction of surface acoustic waves in a Weyl phononic crystal
• Periodic Table for Topological Bands with Non-Hermitian Bernard-LeClair Symmetries
• Topological Hybrid Silicon Microlasers
• Classification of Exceptional Points and Non-Hermitian Topological Semimetals
• Bulk-Boundary Correspondence in a Non-Hermitian System in One Dimension with Chiral-Inversion Symmetry
• Topological properties of linear circuit lattices
• Experimental realization of a Weyl exceptional ring
• Higher-order topological corner states induced by gain and loss
• Topological states of non-Hermitian systems
• PT-symmetry in honeycomb photonic lattices
• Exceptional rings in two-dimensional correlated systems with chiral symmetry
• Non-Hermitian extensions of higher-order topological phases and their biorthogonal bulk-boundary correspondence
• Symmetry-protected nodal phases in non-Hermitian systems
• Defining a bulk-edge correspondence for non-Hermitian Hamiltonians via singular-value decomposition
• Non-Hermitian systems and topology: A transfer-matrix perspective
• Exceptional Surfaces in PT-Symmetric Photonic Systems
• Non-Hermitian higher-order topological states in nonreciprocal and reciprocal systems with their electric-circuit realization
• Perspective on topological states of non-Hermitian lattices
• Exceptional Links and Twisted Fermi Ribbons in non-Hermitian Systems
• Lattice models with exactly solvable topological hinge and corner states
• Knotted Non-Hermitian Metals
• Generalized bulk-edge correspondence for non-hermitian topological systems
• Non-Hermitian Weyl Physics in Topological Insulator Ferromagnet Junctions
• Exceptional points and the topology of quantum many-body spectra
• Hyperbolic Nodal Band Structures and Knot Invariants

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