New topological invariants in non-Hermitian systems

Abstract

Both theoretical and experimental studies of topological phases in non-Hermitian systems have made a remarkable progress in the last few years of research. In this article, we review the key concepts pertaining to topological phases in non-Hermitian Hamiltonians with relevant examples and realistic model setups. Discussions are devoted to both the adaptations of topological invariants from Hermitian to non-Hermitian systems, as well as origins of new topological invariants in the latter setup. Unique properties such as exceptional points and complex energy landscapes lead to new topological invariants including winding number/vorticity defined solely in the complex energy plane, and half-integer winding/Chern numbers. New forms of Kramers degeneracy appear here rendering distinct topological invariants. Modifications of adiabatic theory, time-evolution operator, biorthogonal bulk-boundary correspondence lead to unique features such as topological displacement of particles, `skin-effect', and edge-selective attenuated and amplified topological polarizations without chiral symmetry. Extension and realization of topological ideas in photonic systems are mentioned. We conclude with discussions on relevant future directions, and highlight potential applications of some of these unique topological features of the non-Hermitian Hamiltonians.

28 pages, 11 figures. Invited review article. Typos corrected

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Cited by in corpus (34)

• Efficient Light Funneling based on the non-Hermitian Skin Effect
• Topological acoustics
• Topological phase transition in non-Hermitian quasicrystals
• Observation of parity-time symmetry breaking in a single spin system
• Active topological photonics
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• Localization and topological transitions in non-Hermitian quasiperiodic lattices
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• Nonlinearity induced topological physics in momentum space and real space
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• Non-Hermitian Hartman effect
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• Eigenstate clustering around exceptional points
• Non-Hermitian superconducting diode effect
• Topological invariants of complex energy plane in non-Hermitian systems
• Rigidity of topological invariants to symmetry breakings
• Phase transitions in non-Hermitian superlattices
• Band topology of pseudo-Hermitian phases through tensor Berry connections and quantum metric
• Diffusive Topological Transport in Spatiotemporal Thermal Lattices
• Exploring Metamaterial Lasers through Non-Hermitian Scattering Formalism
• Probing phase transitions in non-Hermitian systems with quantum entanglement
• Simulating monitoring-induced topological phase transitions with small systems
• Self-healing of non-Hermitian topological skin modes