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.

11pages, 7figures

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• 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