A brief review of hybrid skin-topological effect

Abstract

The finding of non-Hermitian skin effect has revolutionized our understanding of non-Hermitian topological phases, where the usual bulk-boundary correspondence is broken and new topological phases specific to non-Hermitian system are uncovered. Hybrid skin-topological effect (HSTE) is a class of newly discovered non-Hermitian topological states that simultaneously supports skin-localized topological edge states and extended bulk states. Here we provide a brief review of HSTE, starting from different mechanics that have been used to realize HSTE, including non-reciprocal couplings, onsite gain/loss, and non-Euclidean lattice geometries. We also review some theoretical developments closely related to the HSTE, including the concept of higher-order non-Hermitian skin effect, parity-time symmetry engineering, and non-Hermitian chiral skin effect. Finally, we summarize recent experimental exploration of HSTE, including its realization in electric circuits systems, non-Hermitian photonic crystals, and active matter systems. We hope this review can make the concept of hybrid-skin effect clearer and inspire new finding of non-Hermitian topological states in higher dimensional systems.

arXiv commentA review article with 13 pages and 9 figures. Comments are welcome

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• A review of active matter reviews
• General criterion for non-Hermitian skin effects and Application: Fock space skin effects in many body systems
• Interaction-Induced Second-Order Skin Effect
• Non-Hermitian Skin Effect Along Hyperbolic Geodesics
• Intrinsic-perturbation induced anomalous higher-order boundary states in non-Hermitian systems
• Anisotropic-scaling localization in higher-dimensional non-Hermitian systems
• Non-Hermitian higher-order topological insulators enabled by altermagnet engineering
• Wiener-Hopf factorization and non-Hermitian topology for Amoeba formulation in one-dimensional multiband systems