Periodic Table for Floquet Topological Insulators

Abstract

Dynamical phases with novel topological properties are known to arise in driven systems of free fermions. In this paper, we obtain a `periodic table' to describe the phases of such time-dependent systems, generalizing the periodic table for static topological insulators. Using K-theory, we systematically classify Floquet topological insulators from the ten Altland-Zirnbauer symmetry classes across all dimensions. We find that the static classification scheme described by a group $G$ becomes $G\times G$ in the time-dependent case, and interpret the two factors as arising from the bipartite decomposition of the unitary time-evolution operator. Topologically protected edge modes may arise at the boundary between two Floquet systems, and we provide a mapping between the number of such edge modes and the topological invariant of the bulk.

16 pages, 2 tables, 2 figures; v2 includes minor changes/corrections and an improved Appendix E

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• Topological classification of non-Hermitian systems with reflection symmetry
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• Geometric aspects of nonlinear and nonequilibrium phenomena
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• Floquet engineering of low-energy dispersions and dynamical localization in a periodically kicked three-band system
• Absolutely Stable Spatiotemporal Order in Noisy Quantum Systems
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• Mixed higher-order topology: boundary non-Hermitian skin effect induced by a Floquet bulk
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• Entanglement spectrum and entropy in Floquet topological matter
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• Quantized Floquet topology with temporal noise
• Wave packet dynamics and edge transport in anomalous Floquet topological phases
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• Topological Defects in Floquet Circuits
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• Theory of Anomalous Floquet Higher-Order Topology: Classification, Characterization, and Bulk-Boundary Correspondence
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• Dynamical Symmetry Indicators for Floquet Crystals
• Immutable quantized transport in Floquet chains
• Universal localization-delocalization transition in chiral-symmetric Floquet drives
• Coupled-wire construction of non-Abelian higher-order topological phases
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• Floquet quantum multiparameter estimation with periodic-driving-induced topological phase transition
• Dynamical Signatures of Floquet Topology in Wave Packet Dynamics
• Phase transitions from Heating to non-heating in SU(1, 1) quantum dynamics: applications to Bose-Einstein condensates and periodically driven coupled oscillators
• Floquet topological systems with flat bands: Edge modes, Berry curvature, and Orbital magnetization
• Quantized Chern-Simons Axion Coupling in Anomalous Floquet Systems