Symmetry and topological classification of Floquet non-Hermitian systems

Abstract

Recent experimental advances in Floquet engineering and controlling dissipation in open systems have brought about unprecedented flexibility in tailoring novel phenomena without any static and Hermitian analogues. It can be epitomized by the various Floquet and non-Hermitian topological phases. Topological classifications of either static/Floquet Hermitian or static non-Hermitian systems based on the underlying symmetries have been well established in the past several years. However, a coherent understanding and classification of Floquet non-Hermitian (FNH) topological phases have not been achieved yet. Here we systematically classify FNH topological bands for 54-fold generalized Bernard-LeClair (GBL)symmetry classes and arbitrary spatial dimensions using $K$-theory. The classification distinguishes two different scenarios of the Floquet operator's spectrum gaps [dubbed as Floquet operator (FO) angle-gapped and FO angle-gapless]. The results culminate into two periodic tables, each containing 54-fold GBL symmetry classes. Our scheme reveals FNH topological phases without any static/Floquet Hermitian and static non-Hermitian counterparts. And our results naturally produce the periodic tables of Floquet Hermitian topological insulators and Floquet unitaries. The framework can also be applied to characterize the topological phases of bosonic systems. We provide concrete examples of one and two-dimensionalfermionic/bosonic systems. And we elucidate the meaning of the topological invariants and their physical consequences. Our paper lays the foundation for a comprehensive exploration of FNH topological bands. And it opens a broad avenue toward uncovering unique phenomena and functionalities emerging from the synthesis of periodic driving, non-Hermiticity, and band topology.

36 pages, 5 figures, 5 tables

References in corpus (24)

• Classification of topological insulators and superconductors in three spatial dimensions
• Making Sense of Non-Hermitian Hamiltonians
• The physics of exceptional points
• Quantum States and Phases in Driven Open Quantum Systems with Cold Atoms
• Topological characterization of periodically-driven quantum systems
• Loss-induced suppression and revival of lasing
• PT-Symmetric Phonon Laser
• Selective enhancement of topologically induced interface states in a dielectric resonator chain
• Weyl Exceptional Rings in a Three-Dimensional Dissipative Cold Atomic Gas
• Tools for quantum simulation with ultracold atoms in optical lattices
• Periodic Table for Topological Bands with Non-Hermitian Bernard-LeClair Symmetries
• $\mathcal{P}\mathcal{T}$-Symmetry-Breaking Chaos in Optomechanics
• New topological invariants in non-Hermitian systems
• Superfluidity of Bose-Einstein Condensate in An Optical Lattice: Landau-Zener Tunneling and Dynamical Instability
• Detecting topological invariants in nonunitary discrete-time quantum walks
• Topological invariants of Floquet systems: General formulation, special properties, and Floquet topological defects
• Tunable Spin-Orbit Coupling via Strong Driving in Ultracold Atom Systems
• Geometric Response and Disclination-Induced Skin Effects in Non-Hermitian Systems
• Dislocation Non-Hermitian Skin Effect
• Stabilizing Non-Hermitian Systems by Periodic Driving
• Random matrices beyond the Cartan classification
• Helical Floquet Channels in 1D Lattices
• Andreev reflection in bosonic condensates
• Squaring the fermion: The threefold way and the fate of zero modes

Cited by in corpus (27)

• Topological Non-Hermitian skin effect
• Non-Hermitian Topological Phases: Principles and Prospects
• Floquet engineering of point-gapped topological superconductors
• Non-Hermitian Floquet Topological Matter -- A Review
• Non-Hermitian strongly interacting Dirac fermions: a quantum Monte-Carlo study
• Loss-induced Floquet non-Hermitian skin effect
• Exact solution of the Bose Hubbard model with unidirectional hopping
• A brief review of hybrid skin-topological effect
• Degeneracies and symmetry breaking in pseudo-Hermitian matrices
• Non-Hermitian Skin Effect in Periodically-Driven Dissipative Ultracold Atoms
• Emergent conservation in Floquet dynamics of integrable non-Hermitian models
• Entanglement phase transitions in non-Hermitian Floquet systems
• Floquet Exceptional Topological Insulator
• Entanglement transitions in a periodically driven non-Hermitian Ising chain
• Anomalous second-order skin modes in Floquet non-Hermitian systems
• Engineering imaginary stark ladder in a dissipative lattice: passive $\mathcal{P}\mathcal{T}$ symmetry, K symmetry and localized damping
• Hilbert space fragmentation imposed real spectrum of non-Hermitian systems
• Topological characterization of a non-Hermitian ladder via Floquet non-Bloch theory
• Berry curvature inside parity-time-symmetry protected exceptional surface
• Topology of Discrete Quantum Feedback Control
• Extended unitarity and absence of skin effect in periodically driven systems
• Space-time symmetry and nonreciprocal parametric resonance in mechanical systems
• Time-dependent driving and topological protection in the fractional Josephson effect
• Breakdown of Non-Bloch Bulk-Boundary Correspondence and Emergent Topology in Floquet Non-Hermitian Systems
• Dynamic manifestation of exception points in a non-Hermitian continuous model with an imaginary periodic potential
• Liouvillian topology and nonreciprocal dynamics in open Floquet chains
• Coupled-wire construction of non-Abelian higher-order topological phases