Non-Hermitian second-order skin and topological modes

Abstract

The skin effect and topological edge states in non-Hermitian system have been well-studied, and the second-order skin effect and corner modes have also been proposed in non-Hermitian system recently. In this paper, we construct the nested tight-binding formalism to research the second-order corner modes analytically, which is a direct description of the generic non-Hermitian tight-binding model without other assumptions. Within this formalism, we obtain the exact solutions of second-order topological zero-energy corner modes for the non-Hermitian four-band model. We validate the nested tight-binding formalism in the hybrid skin-topological corner modes for the four-band model and a non-Hermitian two-dimensional (2D) extrinsic model. In addition, we exactly illustrate the corner modes induced by second-order skin effect for a simplest 2D non-Hermitian model by the nested tight-binding formalism.

15 pages,4 figures

References in corpus (28)

• Topological Insulators with Inversion Symmetry
• Classification of topological insulators and superconductors in three spatial dimensions
• Topological Field Theory of Time-Reversal Invariant Insulators
• Topological Crystalline Insulators
• The physics of exceptional points
• Electric Multipole Moments, Topological Multipole Moment Pumping, and Chiral Hinge States in Crystalline Insulators
• Topological Origin of Non-Hermitian Skin Effects
• $(d-2)$-dimensional edge states of rotation symmetry protected topological states
• Loss-induced suppression and revival of lasing
• Reflection symmetric second-order topological insulators and superconductors
• Visualization of Branch Points in PT-Symmetric Waveguides
• Topological Defects and Gapless Modes in Insulators and Superconductors
• Edge Modes, Degeneracies, and Topological Numbers in Non-Hermitian Systems
• Non-Hermitian bulk-boundary correspondence and auxiliary generalized Brillouin zone theory
• Topology of crystalline insulators and superconductors
• Topological phase transition in non-Hermitian quasicrystals
• Higher-order non-Hermitian skin effect
• Classification of reflection symmetry protected topological semimetals and nodal superconductors
• Non-Hermitian skin modes induced by on-site dissipations and chiral tunneling effect
• Higher-Order Topological Insulator in Twisted Bilayer Graphene
• Non-Bloch band theory of non-Hermitian Hamiltonians in the symplectic class
• Second-order topological non-Hermitian skin effects
• Entanglement and spin squeezing in non-Hermitian phase transitions
• Generalized bulk-edge correspondence for non-hermitian topological systems
• Non-Hermitian Dirac Cones
• Exceptional Topological Insulators
• A generalization of Bloch's theorem for arbitrary boundary conditions: Theory
• Appearance of hinge states in second-order topological insulators via the cutting procedure

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• Topological origin of non-Hermitian skin effect in higher dimensions and uniform spectra
• Geometry-dependent skin effects in reciprocal photonic crystals
• Disorder-driven Phase Transitions of Second-order Non-Hermitian Skin Effects
• Experimental observation of non-Hermitian higher-order skin interface states in topological electric circuits
• Bulk-boundary correspondence in point-gap topological phases
• Connections between the Open-boundary Spectrum and Generalized Brillouin Zone in Non-Hermitian Systems
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• R-DMFT study of a non-Hermitian skin effect for correlated systems: analysis based on a pseudo-spectrum
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• Degeneracy and defectiveness in non-Hermitian systems with open boundary
• Phase transitions and bunching of correlated particles in a non-Hermitian quasicrystal
• Non-Hermitian Topology in Hermitian Topological Matter
• General criterion for non-Hermitian skin effects and Application: Fock space skin effects in many body systems
• Hybrid scale-free skin effect in non-Hermitian systems: A transfer matrix approach
• Modified Generalized-Brillouin-Zone Theory with On-site Disorders
• Correlation effects on non-Hermitian point-gap topology in zero dimension: reduction of topological classification
• Exact formulas of the end-to-end Green's functions in non-Hermitian systems
• Tunable two-dimensional laser arrays with zero-phase locking
• Non-Hermitian second-order topological superconductors
• Universal characteristics of one-dimensional non-Hermitian superconductors
• Braiding Topology of Non-Hermitian Open-Boundary Bands
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• Higher-order Skin Effect through a Hermitian-non-Hermitian Correspondence and Its Observation in an Acoustic Kagome Lattice
• Nontrivial worldline winding in non-Hermitian quantum systems
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• Complex semiclassical theory for non-Hermitian quantum systems
• Anomalous pumping in the non-Hermitian Rice-Mele model
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• Anisotropic-scaling localization in higher-dimensional non-Hermitian systems
• Inner non-Hermitian skin effect on Bethe lattice
• Dissipation Enhanced Unidirectional Transport in Topological Systems
• Topological Invariant for Multi-Band Non-hermitian Systems with Chiral Symmetry
• Spin-dependent gain and loss in photonic quantum spin Hall systems
• Exceptional second-order topological insulators
• Theory for the spectral splitting exponent of exceptional points
• Duality between Generalized Non-Hermitian HN Model in Flat Space and Hermitian System in Curved space
• Non-Hermitian Delocalization Induced by Residue Imaginary Velocity
• Hermitian and non-Hermitian topology in active matter
• Multifractal statistics of non-Hermitian skin effect on the Cayley tree
• Magnetic Control of the Non-Hermitian Skin Effect in Two-Dimensional Lattices
• Non-Hermitian higher-order topological insulators enabled by altermagnet engineering
• Hybrid Higher-Order Skin Topological Modes in the Two-Dimensional Su-Schrieffer-Heeger Model with Nonreciprocal Hoppings
• Non-Hermitian Higher-Order Weyl Semimetals
• Floquet multiple exceptional points with higher-order skin effect
• Scaling rule in critical non-Hermitian skin effect
• Self-healing of non-Hermitian topological skin modes
• Topological Classification of Gapped/Gap-preserving Rational Space-Time Crystal Systems
• Winding-control mechanism of non-Hermitian systems
• Non-Hermitian Higher-Order Dirac Semimetals