Topology in non-Hermitian Chern insulators with skin effect

Abstract

The non-Hermitian skin effect can arise in materials that have asymmetric hoppings between atoms or resonating units, which makes the bulk eigenspectrum sensitive to boundary conditions. When skin effect emerges, eigenstates in the bulk continuum can become localized on the edges, making the distinction between edge and bulk states challenging. We establish the bulk-boundary correspondence for a Chern insulator model with non-Hermitian skin effect by combining two approaches ("non-Bloch" approach and "biorthogonal" approach). Both approaches can suppress the skin effect but they are based on different mathematical tools. A biorthogonal inverse participation ratio is used as a measure to distinguish between bulk states and edge states, and a non-Bloch Chern number is used to characterize the topology and predict the number of topological edge bands. In addition to tangential degeneracies, crossing degeneracies are found to occur between the bulk and edge bands. Their presence enriches the (de)localization behavior of the edge states but does not affect the Chern number. The phase diagram of the system has interesting features that are not found in Hermitian systems. For example, one topological transition and two non-Hermitian phase transitions can be induced by tuning a single parameter. The gapless phase is topologically protected due to the stable existence of the non-Hermitian band degeneracies guaranteed by nonzero discriminant numbers.

8 pages, 4 figures

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• Geometry-dependent skin effects in reciprocal photonic crystals
• Hybrid higher-order skin-topological effect in hyperbolic lattices
• Anderson transition at complex energies in one-dimensional parity-time-symmetric disordered systems
• Anderson Delocalization in Strongly Coupled Disordered Non-Hermitian Chains
• Non-Hermitian skin effect enforced by nonsymmorphic symmetries
• Anomalous pumping in the non-Hermitian Rice-Mele model
• Topological Invariant for Multi-Band Non-hermitian Systems with Chiral Symmetry
• Localization transition in non-Hermitian systems depending on reciprocity and hopping asymmetry
• Boundary-driven many-body phase transitions in a non-Hermitian disordered fermionic chain
• Restoration of non-Hermitian bulk-boundary correspondence by counterbalancing skin effect
• Recognizing critical lines via entanglement in non-Hermitian systems
• Exceptional second-order topological insulators
• Tailoring Corner States and Exceptional Points in Altermagnets
• Recurrence method in Non-Hermitian Systems