Non-Hermitian Floquet Topological Matter -- A Review

Abstract

The past few years have witnessed a surge of interest in non-Hermitian Floquet topological matters due to their exotic properties resulting from the interplay between driving fields and non-Hermiticity. The present review sums up our studies on non-Hermitian Floquet topological matters in one and two spatial dimensions. We first give a bird's-eye view of the literature for clarifying the physical significance of non-Hermitian Floquet systems. We then introduce, in a pedagogical manner, a number of useful tools tailored for the study of non-Hermitian Floquet systems and their topological properties. With the aid of these tools, we present typical examples of non-Hermitian Floquet topological insulators, superconductors, and quasicrystals, with a focus on their topological invariants, bulk-edge correspondences, non-Hermitian skin effects, dynamical properties, and localization transitions. We conclude this review by summarizing our main findings and presenting our vision of future directions.

86 pages, 10 figures, submitted

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• Topological $\pi$ modes and beyond

Cited by in corpus (30)

• Floquet engineering of point-gapped topological superconductors
• Emergent entanglement phase transitions in non-Hermitian Aubry-André-Harper chains
• Ring Structure in the Complex Plane: A Fingerprint of non-Hermitian Mobility Edge
• Entanglement phase transitions in non-Hermitian quasicrystals
• Generalized bulk-boundary correspondence in periodically driven non-Hermitian systems
• A brief review of hybrid skin-topological effect
• Phase transitions and bunching of correlated particles in a non-Hermitian quasicrystal
• The non-Hermitian skin effect: A perspective
• Asymmetric transfer matrix analysis of Lyapunov exponents in one-dimensional non-reciprocal quasicrystals
• Floquet topological superconductors with many Majorana edge modes: topological invariants, entanglement spectrum and bulk-edge correspondence
• Entanglement phase transitions in non-Hermitian Floquet systems
• Dynamics and Phases of Nonunitary Floquet Transverse-Field Ising Model
• Direct measurement of topological invariants through temporal adiabatic evolution of bulk states in the synthetic Brillouin zone
• Biorthogonal topological charge pumping in non-Hermitian systems
• Gapless higher-order topology and corner states in Floquet systems
• Non-Bloch Theory for Spatiotemporal Photonic Crystals Assisted by Continuum Effective Medium
• Multiple topological transitions and spectral singularities in non-Hermitian Floquet systems
• Entanglement phase transitions in non-Hermitian Kitaev chains
• Floquet non-Abelian topological charges and edge states
• Retrieving maximum information of symmetric states from their corrupted copies
• Quantum geometry and geometric entanglement entropy of one-dimensional Floquet topological matter
• Floquet Möbius topological insulators
• Exceptional points in SSH-like models with hopping amplitude gradient
• Tailoring higher-order van Hove singularities in non-Hermitian interface systems via Floquet engineering
• Superiority of Krylov shadow tomography in estimating quantum Fisher information: From bounds to exactness
• Breakdown of Non-Bloch Bulk-Boundary Correspondence and Emergent Topology in Floquet Non-Hermitian Systems
• Topology and edge modes surviving criticality in non-Hermitian Floquet systems
• Coupled-wire construction of non-Abelian higher-order topological phases
• Non-Hermitian Floquet dynamics in absorption spectroscopy
• Liouvillian topology and nonreciprocal dynamics in open Floquet chains