Non-Bloch bands in two-dimensional non-Hermitian systems

Abstract

The non-Bloch band theory can describe energy bands in a one-dimensional (1D) non-Hermitian system. On the other hand, whether the non-Bloch band theory can be extended to higher-dimensional non-Hermitian systems is nontrivial. In this work, we construct the non-Bloch band theory in two classes of two-dimensional non-Hermitian systems, by reducing the problem to that for a 1D non-Hermitian model. In these classes of systems, we get the generalized Brillouin zone for a complex wavevector and investigate topological properties. In the model of the non-Hermitian Chern insulator, as an example, we show the bulk-edge correspondence between the Chern number defined from the generalized Brillouin zone and the appearance of the edge states.

arXiv comment11pages, 7figures

References in corpus (64)

• Edge states and topological invariants of non-Hermitian systems
• Non-Hermitian Physics
• Chern Numbers in Discretized Brillouin Zone: Efficient Method of Computing (Spin) Hall Conductances
• Symmetry and Topology in Non-Hermitian Physics
• Topological Origin of Non-Hermitian Skin Effects
• Topological Band Theory for Non-Hermitian Hamiltonians
• 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
• Efficient Light Funneling based on the non-Hermitian Skin Effect
• Edge Modes, Degeneracies, and Topological Numbers in Non-Hermitian Systems
• Non-Hermitian skin effect and chiral damping in open quantum systems
• 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
• Non-reciprocal robotic metamaterials
• Hybrid higher-order skin-topological modes in non-reciprocal systems
• Second-Order Topological Phases in Non-Hermitian Systems
• Critical non-Hermitian Skin Effect
• Universal non-Hermitian skin effect in two and higher dimensions
• 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
• Probing non-Hermitian Skin Effect and non-Bloch Phase Transitions
• Higher-order non-Hermitian skin effect
• Acoustic non-Hermitian skin effect from twisted winding topology
• Observation of higher-order non-Hermitian skin effect
• Non-Hermitian skin modes induced by on-site dissipations and chiral tunneling effect
• Higher-order topological corner states induced by gain and loss
• Non-Hermitian Morphing of Topological Modes
• Exponentially-enhanced quantum sensing with non-Hermitian lattice dynamics
• Second-order topological non-Hermitian skin effects
• Anomalous helical edge states in a non-Hermitian Chern insulator
• Realization of active metamaterials with odd micropolar elasticity
• Hall Conductance of a Non-Hermitian Chern Insulator
• Non-Hermitian Dirac Cones
• Non-Hermitian second-order skin and topological modes
• Hybrid skin-topological modes without asymmetric couplings
• Guided accumulation of active particles by topological design of a second-order skin effect
• Complex Skin Modes in Non-Hermitian Coupled Laser Arrays
• Electric circuits for non-Hermitian Chern insulators
• Non-Hermitian skin effect and self-acceleration
• Second-order topological phases protected by chiral symmetry
• Non-Bloch band theory in bosonic Bogoliubov-de Gennes systems
• Experimental identification of the second-order non-Hermitian skin effect with physics-graph-informed machine learning
• Loss of Hall Conductivity Quantization in a Non-Hermitian Quantum Anomalous Hall Insulator
• Topological semimetal phase with exceptional points in one-dimensional non-Hermitian systems
• Non-Hermitian band topology with generalized inversion symmetry
• Topology and Observables of the Non-Hermitian Chern Insulator
• Non-Hermitian waves in a continuous periodic model and application to photonic crystals
• Non-Bloch band theory and bulk-edge correspondence in non-Hermitian systems
• $\mathcal{P}\mathcal{T}$-Symmetric Topological Edge-Gain Effect
• Geometry-dependent skin effects in reciprocal photonic crystals
• Inversion symmetric non-Hermitian Chern insulator
• Topology in non-Hermitian Chern insulators with skin effect
• Wannier-type photonic higher-order topological corner states induced solely by gain and loss
• Evidencing non-Bloch dynamics in temporal topolectrical circuits
• Non-Hermitian topological exciton-polariton corner modes
• Universal Hall conductance scaling in non-Hermitian Chern insulators
• Two-dimensional anisotropic non-Hermitian Lieb lattice
• Unravelling the edge spectra of non-Hermitian Chern insulators
• Scaling rule in critical non-Hermitian skin effect
• Self-healing of non-Hermitian topological skin modes

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• Experimental Realization of Geometry-Dependent Skin Effect in a Reciprocal Two-Dimensional Lattice
• Non-Hermitian Chiral Skin Effect
• Dynamical Degeneracy Splitting and Directional Invisibility in Non-Hermitian Systems
• Hermitian Bulk -- Non-Hermitian Boundary Correspondence
• Giant Emitters in a Structured Bath with Non-Hermitian Skin Effect
• Edge theory of non-Hermitian skin modes in higher dimensions
• Phase transitions and bunching of correlated particles in a non-Hermitian quasicrystal
• Hybrid scale-free skin effect in non-Hermitian systems: A transfer matrix approach
• Geometry-dependent skin effect and anisotropic Bloch oscillations in a non-Hermitian optical lattice
• Critical non-Hermitian topology induced quantum sensing
• Algebraic non-Hermitian skin effect and generalized Fermi surface formula in arbitrary dimensions
• Nontrivial worldline winding in non-Hermitian quantum systems
• Role of Topology in Relaxation of One-Dimensional Stochastic Processes
• Extended imaginary gauge transformation in a general nonreciprocal lattice
• Anomalous second-order skin modes in Floquet non-Hermitian systems
• Universal spectral moment theorem and its applications in non-Hermitian systems
• Unconventional and robust light-matter interactions based on the non-Hermitian skin effect
• Non-Bloch Dirac Points and Phase Diagram in the Stacked Non-Hermitian SSH Model
• Non-Bloch Theory for Spatiotemporal Photonic Crystals Assisted by Continuum Effective Medium
• Two-dimensional lattice with an imaginary magnetic field
• Optical non-Hermitian skin effect in two-dimensional uniform media
• General corner charge formulas in various tetrahedral and cubic space groups
• Non-Hermitian Delocalization Induced by Residue Imaginary Velocity
• Hermitian and non-Hermitian topology in active matter
• Experimentally Probing Non-Hermitian Spectral Transition and Eigenstate Skewness
• Tailoring Corner States and Exceptional Points in Altermagnets
• Topological photonics in nanoscaled systems with far field radiation and polarization singularities
• Optimal spectral transport of non-Hermitian systems
• Wiener-Hopf factorization and non-Hermitian topology for Amoeba formulation in one-dimensional multiband systems