Exact Solutions Disentangle Higher-Order Topology in 2D Non-Hermitian Lattices

Abstract

We report the exact closed-form solutions for higher-order topological states as well as explicit energy-spectrum relationships in two-dimensional (2D) non-Hermitian multi-orbital lattices with generalized boundary conditions. These analytical solutions unequivocally confirm that topological edge states in a 2D non-Hermitian system which feature point-gap topology must undergo the non-Hermitian skin effect along the edge. Under double open boundary conditions, the occurrence of the non-Hermitian skin effect for either topological edge states or bulk states can be accurately predicted by our proposed winding numbers. We unveil that the zero-energy topological corner state only manifests itself on a corner where two nearby gapped edge states intersect, and thus can either disappear completely or strengthen drastically due to the non-Hermitian skin effect of gapped topological edge states. Our analytical results offer direct insight into the non-Bloch band topology in two or higher dimensions and trigger experimental investigations into related phenomena such as quadrupole topological insulators and topological lasing.

References in corpus (70)

• Topological insulators and superconductors
• Experimental Observation of Quantum Hall Effect and Berry's Phase in Graphene
• Topological Photonics
• A topological Dirac insulator in a quantum spin Hall phase : Experimental observation of first strong topological insulator
• Classification of topological quantum matter with symmetries
• Edge states and topological invariants of non-Hermitian systems
• Exceptional Topology of Non-Hermitian Systems
• Non-Hermitian Physics
• Colloquium: Topological Band Theory
• Localization transitions in non-Hermitian quantum mechanics
• Symmetry and Topology in Non-Hermitian Physics
• Topological Origin of Non-Hermitian Skin Effects
• Non-Bloch Band Theory of Non-Hermitian Systems
• Topolectrical circuit realization of topological corner modes
• Observation of a phononic quadrupole topological insulator
• Correspondence between winding numbers and skin modes in non-hermitian systems
• Nonlocal edge state transport in the quantum spin Hall state
• Non-Hermitian Boundary Modes
• Anatomy of skin modes and topology in non-Hermitian systems
• Tunable Correlated Chern Insulator and Ferromagnetism in Trilayer Graphene/Boron Nitride Moiré Superlattice
• The space group classification of topological band insulators
• Topolectrical circuits
• Topological classification of crystalline insulators through band structure combinatorics
• Visualization of higher-order topological insulating phases in two-dimensional dielectric photonic crystals
• Fractional Chern Insulator
• Direct observation of corner states in second-order topological photonic crystal slabs
• Complex Edge-State Phase Transitions in 1D Topological Laser Arrays
• Classical higher-order topological insulators
• Second-order photonic topological insulator with corner states
• Hybrid higher-order skin-topological modes in non-reciprocal systems
• Non-reciprocal robotic metamaterials
• Second-Order Topological Phases in Non-Hermitian Systems
• Novel Topological Phase with Zero Berry Curvature
• Critical non-Hermitian Skin Effect
• Topological acoustics
• Topological phase transition in non-Hermitian quasicrystals
• Universal non-Hermitian skin effect in two and higher dimensions
• Non-Hermitian Topological Sensors
• 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
• Observation of higher-order non-Hermitian skin effect
• Topological quantum matter with cold atoms
• Topology-Induced Spontaneous Non-reciprocal Pumping in Cold-Atom Systems with Loss
• Exact solution of non-Hermitian systems with generalized boundary conditions: size-dependent boundary effect and fragility of skin effect
• Helical Topological Edge States in a Quadrupole Phase
• Second-order topological non-Hermitian skin effects
• Topological defect engineering and PT-symmetry in non-Hermitian electrical circuits
• Non-Hermitian route to higher-order topology in an acoustic crystal
• Topological states in non-Hermitian two-dimensional Su-Schrieffer-Heeger model
• Non-integer optical modes in a Möbius-ring resonator
• Evidence for Higher order topology in Bi and Bi${}_{0.92}$Sb${}_{0.08}$
• Exceptional Bound States and negative Entanglement Entropy
• Experimental Observation of Berry Phases in Optical Moebius-strip Microcavities
• Experimental identification of the second-order non-Hermitian skin effect with physics-graph-informed machine learning
• Twisted quadrupole topological photonic crystals
• Higher-order topological band structures
• Dimensional transmutation from non-Hermiticity
• Realization of quasicrystalline quadrupole topological insulators in electrical circuits
• Zoology of non-Hermitian spectra and their graph topology
• Sensitivity of non-Hermitian systems
• Photonic realization of a generic type of graphene edge states exhibiting topological flat band
• Higher-Order Topological In-Bulk Corner State in Pure Diffusion Systems
• Topological edge and corner states in Bi fractals on InSb
• Observation of higher-order topological states on a quantum computer
• Percolation-induced PT symmetry breaking
• Activating non-Hermitian skin modes by parity-time symmetry breaking
• Breaking and resurgence of symmetry in the non-Hermitian Su-Schrieffer-Heeger model in photonic waveguides
• Topological Flat Bands in Graphene Super-moiré Lattices
• Observation of non-local impedance response in a passive electrical circuit

Cited by in corpus (7)

• Non-Hermitian Second-Order Topological Phases and Bipolar Skin Effect in Photonic Kagome Crystals
• Non-Hermitian ultra-strong bosonic clustering through interaction-induced caging
• Quasiparticle picture of topological phase transitions induced by interactions
• Size-Dependent Skin Effect Transitions in Weakly Coupled Non-Reciprocal Chains
• Interacting many-body non-Hermitian systems as Markov chains
• Wiener-Hopf factorization and non-Hermitian topology for Amoeba formulation in one-dimensional multiband systems
• Quasiperiodic Skin Criticality in an Exactly Solvable Non-Hermitian Quasicrystal