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 (12)

• Topological Photonics
• A topological Dirac insulator in a quantum spin Hall phase : Experimental observation of first strong topological insulator
• Topological Origin of Non-Hermitian Skin Effects
• Nonlocal edge state transport in the quantum spin Hall state
• The space group classification of topological band insulators
• Visualization of higher-order topological insulating phases in two-dimensional dielectric photonic crystals
• Direct observation of corner states in second-order topological photonic crystal slabs
• Novel Topological Phase with Zero Berry Curvature
• Topological acoustics
• Topological phase transition in non-Hermitian quasicrystals
• Topological states in non-Hermitian two-dimensional Su-Schrieffer-Heeger model
• Evidence for Higher order topology in Bi and Bi${}_{0.92}$Sb${}_{0.08}$

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