Perspective on topological states of non-Hermitian lattices

Abstract

The search of topological states in non-Hermitian systems has gained a strong momentum over the last two years climbing to the level of an emergent research front. In this Perspective we give an overview with a focus in connecting this topic to others like Floquet systems. Furthermore, using a simple scattering picture we discuss an interpretation of concepts like the Hamiltonian's defectiveness, i.e. the lack of a full basis of eigenstates, crucial in many discussions of topological phases of non-Hermitian Hamiltonians.

22 pages, 4 figures, invited article to appear in Journal of Physics: Materials, special issue

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• Knots and Non-Hermitian Bloch Bands
• Non-Hermitian band topology and skin modes in active elastic media
• The 2021 Quantum Materials Roadmap
• Non-Bloch band collapse and chiral Zener tunneling
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• Controlling mass and energy diffusion with metamaterials
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• Hybrid skin-topological modes without asymmetric couplings
• Dynamics and topology of non-Hermitian elastic lattices with non-local feedback control interactions
• Guided accumulation of active particles by topological design of a second-order skin effect
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• Non-Hermitian Photonic Lattices: tutorial
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• Non-normal Hamiltonian dynamics in quantum systems and its realization on quantum computers
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• Topological transitions in quantum jump dynamics: Hidden exceptional points
• Nonsymmetric evanescent coupling in photonics
• Versatile Braiding of Non-Hermitian Topological Edge States
• Selective and tunable excitation of topological non-Hermitian skin modes
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• Exceptional flat bands in bipartite non-Hermitian lattices
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