Non-Hermitian Topological Phases: Principles and Prospects

Abstract

The synergy between non-Hermitian concepts and topological ideas have led to very fruitful activity in the recent years. Their interplay has resulted in a wide variety of new non-Hermitian topological phenomena being discovered. In this review, we present the key principles underpinning the topological features of non-Hermitian phases. Using paradigmatic models -- Hatano-Helson, non-Hermitian Su-Schrieffer-Heeger and non-Hermitian Chern insulator -- we illustrate the central features of non-Hermitian topological systems, including exceptional points, complex energy gaps and non-Hermitian symmetry classification. We discuss the non-Hermitian skin effect and the notion of the generalized Brillouin zone, which allows restoring the bulk-boundary correspondence. Using concrete examples, we examine the role of disorder, present the linear response framework, and analyze the Hall transport properties of non-Hermitian topological systems. We also survey the rapidly growing experimental advances in this field. Finally, we end by highlighting possible directions which, in our view, may be promising for explorations in the near future.

arXiv commentTopical review. Close to published version

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Cited by in corpus (37)

• Anomalous Skin Effects in Disordered Systems with a Single non-Hermitian Impurity
• Non-Hermitian Floquet Topological Matter -- A Review
• Generalized bulk-boundary correspondence in periodically driven non-Hermitian systems
• Erratic non-Hermitian skin localization
• Entanglement dynamics in the many-body Hatano-Nelson model
• Incoherent non-Hermitian skin effect in photonic quantum walks
• A brief review of hybrid skin-topological effect
• Phase transitions and bunching of correlated particles in a non-Hermitian quasicrystal
• Engineering non-Hermitian Second Order Topological Insulator in Quasicrystals
• Emergence of tunable exceptional points in altermagnet-ferromagnet junctions
• Topological phases of commensurate or incommensurate non-Hermitian Su-Schrieffer-Heeger lattices
• Spectral structure and doublon dissociation in the two-particle non-Hermitian Hubbard model
• Real-space topological localizer index to fully characterize the dislocation skin effect
• Dynamics and Phases of Nonunitary Floquet Transverse-Field Ising Model
• Floquet Exceptional Topological Insulator
• Entangelment Entropy on Generalized Brillouin Zone
• Majorana zero-modes in a dissipative Rashba nanowire
• Edge-selective extremal damping from topological heritage of dissipative Chern insulators
• Néel vector controlled exceptional contours in $p$-wave magnet-ferromagnet junctions
• Measuring Non-Hermitian Topological Invariants Directly from Quench Dynamics
• Liouvillian skin effect in quantum neural networks
• Transfer learning from Hermitian to non-Hermitian quantum many-body physics
• Non-Hermitian dynamical topological winding in photonic mesh lattices
• Quantum Pontus-Mpemba Effect Enabled by the Liouvillian Skin Effect
• Measuring topological invariants of even-dimensional line-gapped non-Hermitian systems through quench dynamics
• Uncovering Exceptional Contours in non-Hermitian Hyperbolic Matter
• Magnetic Control of the Non-Hermitian Skin Effect in Two-Dimensional Lattices
• Tailoring higher-order van Hove singularities in non-Hermitian interface systems via Floquet engineering
• Adiabatic charge transport through non-Bloch bands
• Recent progress on disorder-induced topological phases
• Computation and Verification of Spectra for Non-Hermitian Systems
• Magnetic field effects on the Kitaev model coupled to environment
• Hexagonal Warping Control of Exceptional Points in Topological Insulator--Ferromagnetic Heterojunctions
• Nonreciprocal Floquet tunneling dynamics of spin-orbit-coupled bosonic atoms in a non-Hermitian double-well potential
• Continuum Landau surface states in a non-Hermitian Weyl semimetal
• Coupled-wire construction of non-Abelian higher-order topological phases
• Characterizing Liouvillian Exceptional Points Through Newton Polygons and Tropical Geometry